Criteria for Algebraic Operators to be Unitary

被引：3

作者：

Jablonski, Zenon Jan ^{[1
]}

Stochel, Jan ^{[1
]}

Jung, Il Bong ^{[2
]}

机构：

[1] Uniwersytet Jagiellonski, Inst Matematyki, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea

来源：

KYUNGPOOK MATHEMATICAL JOURNAL | 2023年 / 63卷 / 01期

关键词：

Secondary Key words and phrases; Algebraic operator; unitary operator; normaloid operator; strong stability; M-ISOMETRIC TRANSFORMATIONS;

D O I：

10.5666/KMJ.2022.63.1.1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By the spectral theorem, a unitary operator with a finite spectrum is algebraic and its spectrum is contained in T, the unit circle centered at 0. The most fundamental example of a unitary algebraic operator is the Fourier transform. According to the famous theorem of Plancherel, the Fourier transform extends uniquely to a unitary operator on L2(R) (see e.g., [18, Theorem IX.6]). Denote it by ". The Fourier transform has the following properties:

引用

页码：1 / 10

页数：10

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