{"id":4106,"date":"2025-04-15T07:58:12","date_gmt":"2025-04-15T07:58:12","guid":{"rendered":"https:\/\/fs.kibu.ac.ke\/?p=4106"},"modified":"2025-12-27T00:28:07","modified_gmt":"2025-12-27T00:28:07","slug":"equivalent-characterizations-of-isometrically-bounded-operators-with-circular-numerical-ranges","status":"publish","type":"post","link":"https:\/\/kibu.ac.ke\/fs\/equivalent-characterizations-of-isometrically-bounded-operators-with-circular-numerical-ranges\/","title":{"rendered":"Equivalent Characterizations of Isometrically Bounded Operators with Circular Numerical Ranges"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"4106\" class=\"elementor elementor-4106\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4ef2018d elementor-section-full_width elementor-section-height-min-height elementor-section-items-stretch elementor-section-height-default\" data-id=\"4ef2018d\" data-element_type=\"section\" id=\"ourgoal\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-13fb9aea\" data-id=\"13fb9aea\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5dba698 elementor-widget elementor-widget-theme-post-title elementor-page-title elementor-widget-heading\" data-id=\"5dba698\" data-element_type=\"widget\" data-widget_type=\"theme-post-title.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Equivalent Characterizations of Isometrically Bounded Operators with Circular Numerical Ranges<\/h1>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5b5bb18f elementor-section-height-min-height elementor-section-boxed elementor-section-height-default elementor-section-items-middle\" data-id=\"5b5bb18f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-40122eec\" data-id=\"40122eec\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-33df3e6f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"33df3e6f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-6286bd1b elementor-invisible\" data-id=\"6286bd1b\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7b5a4440 elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"7b5a4440\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">2024<\/h2>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-991f06b elementor-invisible\" data-id=\"991f06b\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6be99d6d elementor-widget elementor-widget-heading\" data-id=\"6be99d6d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">KIBU Authors<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b02b2d5 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"1b02b2d5\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p>Shem Aywa<\/p><p>John Sirengo<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-7ab6e768 elementor-invisible\" data-id=\"7ab6e768\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-26805b51 elementor-tablet-align-left elementor-invisible elementor-widget elementor-widget-button\" data-id=\"26805b51\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeInLeft&quot;}\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-shrink\" href=\"https:\/\/www.irejournals.com\/paper-details\/1706065\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">VIEW ON PUBLISHER SITE<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-379a27e1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"379a27e1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-f5bdf1c elementor-invisible\" data-id=\"f5bdf1c\" data-element_type=\"column\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;,&quot;animation&quot;:&quot;fadeIn&quot;,&quot;animation_mobile&quot;:&quot;none&quot;}\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-30e4604 elementor-widget elementor-widget-heading\" data-id=\"30e4604\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Abstract<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5e436d52 elementor-invisible elementor-widget elementor-widget-text-editor\" data-id=\"5e436d52\" data-element_type=\"widget\" data-settings=\"{&quot;_animation&quot;:&quot;fadeIn&quot;}\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<div class=\"card indipaper-list-c1\"><div class=\"card-body\"><div class=\"row\"><div class=\"col-md-10\"><p class=\"text-justify\">This study investigates the equivalent characterizations of isometrically bounded operators with circular numerical ranges on complex Hilbert spaces. The main objective is to establish necessary and sufficient conditions for an isometrically bounded operator to have a circular numerical range and to explore the connections between circularity and unitary equivalence, scalar multiples of unitary operators, and scalar multiples of isometries. The study employs a comprehensive theoretical framework that combines techniques from functional analysis, operator theory, and convex geometry to derive the main results. The key findings include a complete characterization of isometrically bounded operators with circular numerical ranges in terms of their unitary equivalence and representation as scalar multiples of unitary operators or isometries. The study also presents several related results on the spectral properties and geometric structure of these operators. Furthermore, the research highlights the potential applications of the findings in quantum mechanics and matrix analysis, where the circularity of numerical ranges plays a crucial role. The study makes significant contributions to the understanding of isometrically bounded operators and their numerical ranges, providing a unified and generalized framework for analyzing their properties and behavior. The results and techniques developed in this research have the potential to inspire new approaches to problems in operator theory and related fields, and to lead to the development of novel algorithms and tools for studying the geometry of numerical ranges.<\/p><\/div><\/div><\/div><\/div><div class=\"card indipaper-list-c1\"><div class=\"card-body\"><div class=\"row\"><div class=\"col-md-1\">\u00a0<\/div><div class=\"col-md-10\"><h5 class=\"card-subtitle mb-2\">Keywords<\/h5><p class=\"text-justify\">Equivalent Characterizations, Isometrically Bounded Operators, Circular Numerical Ranges<\/p><\/div><\/div><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>2024 KIBU Authors Shem Aywa John Sirengo VIEW ON PUBLISHER SITE Abstract This study investigates the equivalent characterizations of isometrically bounded operators with circular numerical ranges on complex Hilbert spaces. The main objective is to establish necessary and sufficient conditions for an isometrically bounded operator to have a circular numerical range and to explore the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_header_footer","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4106","post","type-post","status-publish","format-standard","hentry","category-research-list"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Equivalent Characterizations of Isometrically Bounded Operators with Circular Numerical Ranges - Faculty of Science<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/kibu.ac.ke\/fs\/equivalent-characterizations-of-isometrically-bounded-operators-with-circular-numerical-ranges\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Equivalent Characterizations of Isometrically Bounded Operators with Circular Numerical Ranges - Faculty of Science\" \/>\n<meta property=\"og:description\" content=\"2024 KIBU Authors Shem Aywa John Sirengo VIEW ON PUBLISHER SITE Abstract This study investigates the equivalent characterizations of isometrically bounded operators with circular numerical ranges on complex Hilbert spaces. 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