Scholarlink

<p>A bounded linear operator <i>T</i> on a Hilbert space <i>H</i> is said to be orbital frame if there exists a vector <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40995_2025_1780_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(x \in H\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>∈</mo> <mi>H</mi> </mrow> </math></EquationSource> </InlineEquation> such that <i>orb</i>(<i>T</i>,&#xa0;<i>x</i>) is a frame. This paper presents a new examination of frames in the context of Hilbert spaces, showing that orbital frames operators must be Fredholm. In particular, if an orbital frame operator either has a dense range or be one-to-one then it is an invertible.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fredholm Nature of Orbital Frame Operators in Hilbert Spaces

  • 期刊论文

  • 发表日期：

    2025年3月10日

查看全文
  • Z. Saeedi,
  • H. Rezaei

摘要

A bounded linear operator T on a Hilbert space H is said to be orbital frame if there exists a vector \(x \in H\) x ∈ H such that orb(T, x) is a frame. This paper presents a new examination of frames in the context of Hilbert spaces, showing that orbital frames operators must be Fredholm. In particular, if an orbital frame operator either has a dense range or be one-to-one then it is an invertible.