1. bookVolume 2021 (2021): Issue 1 (January 2021)
Journal Details
License
Format
Journal
eISSN
2544-9990
First Published
30 May 2018
Publication timeframe
1 time per year
Languages
English
access type Open Access

Some notes on complex symmetric operators

Published Online: 04 Dec 2021
Volume & Issue: Volume 2021 (2021) - Issue 1 (January 2021)
Page range: 90 - 96
Received: 11 Nov 2020
Accepted: 21 Nov 2021
Journal Details
License
Format
Journal
eISSN
2544-9990
First Published
30 May 2018
Publication timeframe
1 time per year
Languages
English
Abstract

In this paper we show that every conjugation C on the Hardy-Hilbert space H2 is of type C = T *𝒥T, where T is an unitary operator and 𝒥f(z)=f(z¯)¯ \mathcal{J}f\left( z \right) = \overline {f\left( {\bar z} \right)} with f ∈ H2. Moreover we prove some relations of complex symmetry between the operators T and |T|, where T = U |T| is the polar decomposition of bounded operator T ∈ ℒ(ℋ) on the separable Hilbert space ℋ.

Keywords

MSC 2010

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