<p>The paper delves into several characterizations of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{A}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">A</mi> </math></EquationSource> </InlineEquation>-approximate point spectrum of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{A}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">A</mi> </math></EquationSource> </InlineEquation>-bounded operators acting on a complex semi-Hilbertian space <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq8.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{H}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">H</mi> </math></EquationSource> </InlineEquation> and also investigates properties of the <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{A}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">A</mi> </math></EquationSource> </InlineEquation>-approximate point spectrum for the tensor product of two <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq10.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{A}^{\frac{1}{2}}$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="italic">A</mi> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </msup> </math></EquationSource> </InlineEquation>-adjoint operators. Furthermore, several properties of <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_831_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\textit{A}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="italic">A</mi> </math></EquationSource> </InlineEquation>-normal operators have been established.</p>

$\textit{A}$-approximate point spectrum of $\textit{A}$-bounded operators in semi-Hilbertian spaces

期刊论文
发表日期：

2025年7月6日

查看全文

Arup Majumdar,
P. Sam Johnson

摘要

The paper delves into several characterizations of $\textit{A}$ $A$ -approximate point spectrum of $\textit{A}$ $A$ -bounded operators acting on a complex semi-Hilbertian space $\textit{H}$ $H$ and also investigates properties of the $\textit{A}$ $A$ -approximate point spectrum for the tensor product of two $\textit{A}^{\frac{1}{2}}$ $A^{\frac{1}{2}}$ -adjoint operators. Furthermore, several properties of $\textit{A}$ $A$ -normal operators have been established.

\(\textit{A}\)-approximate point spectrum of \(\textit{A}\)-bounded operators in semi-Hilbertian spaces

摘要