Fredholm Nature of Orbital Frame Operators in Hilbert Spaces

IF 1.4 4区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES

Iranian Journal of Science and Technology, Transactions A: Science Pub Date : 2025-03-10 DOI:10.1007/s40995-025-01780-7

Z. Saeedi, H. Rezaei

引用次数: 0

Abstract

A bounded linear operator T on a Hilbert space H is said to be orbital frame if there exists a vector \(x \in H\) 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.

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Hilbert空间中轨道坐标系算子的Fredholm性质

如果存在一个向量\(x \in H\)使得orb（T, x）是一个坐标系，那么希尔伯特空间H上的有界线性算子T就是轨道坐标系。本文给出了Hilbert空间中对帧的一种新的检验，证明了轨道帧算子必须是Fredholm算子。特别地，如果一个轨道系算符要么有密集的范围，要么是一对一的，那么它是可逆的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Iranian Journal of Science and Technology, Transactions A: Science MULTIDISCIPLINARY SCIENCES-

CiteScore

4.00

自引率

5.90%

发文量

122

审稿时长

>12 weeks

期刊介绍： The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences