Fuglede-Putnam type commutativity theorems for $ EP $ operators

نویسندگان

چکیده

Fuglede-Putnam theorem is not true in general for $ EP operators on Hilbert spaces. We prove that under some conditions the holds good. If adjoint operation replaced by Moore-Penrose inverse theorem, we get type -- however proofs are totally different. Finally, interesting results have been proved using several versions of theorems

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Asymmetric Putnam–fuglede Theorem for Unbounded Operators

The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.

متن کامل

FUGLEDE-PUTNAM THEOREM FOR w-HYPONORMAL OR CLASS Y OPERATORS

An asymmetric Fuglede-Putnam’s Theorem for w−hyponormal operators and class Y operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.

متن کامل

On the Putnam-Fuglede theorem

We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpo-tents. Some asymptotic results are also given.

متن کامل

THE FUGLEDE–PUTNAM THEOREM AND PUTNAM’S INEQUALITY FOR QUASI-CLASS (A, k) OPERATORS

An operator T ∈ B(H) is called quasi-class (A, k) if T ∗k(|T | − |T |)T k ≥ 0 for a positive integer k, which is a common generalization of class A. The famous Fuglede–Putnam’s theorem is as follows: the operator equation AX = XB implies A∗X = XB∗ when A and B are normal operators. In this paper, firstly we show that if X is a Hilbert-Schmidt operator, A is a quasi-class (A, k) operator and B∗ ...

متن کامل

The Fuglede Commutativity Theorem modulo the Hilbert-schmidt Class and Generating Functions for Matrix Operators. I

We prove the following statements about bounded linear operators on a separable, complex Hilbert space: (1) Every normal operator N that is similar to a Hilbert-Schmidt perturbation of a diagonal operator D is unitarily equivalent to a Hilbert-Schmidt perturbation of D; (2) For every normal operator A', diagonal operator D and bounded operator X, the Hilbert-Schmidt norms (finite or infinite) o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Malaya journal of matematik

سال: 2021

ISSN: ['2319-3786', '2321-5666']

DOI: https://doi.org/10.26637/mjm0901/0124