Quasinormality and Fuglede-Putnam Theorem for w-Hyponormal Operators

Mohammad H.M. Rashid

Abstract


We investigate several properties of Aluthge transform $\tT=|T|^{\frac{1}{2}}U|T|^{\frac{1}{2}}$ of an operator $T=U|T|$ . We prove (i) if $T$ is a $w$-hyponormal operatorand $\tT$ is quasi-normal (resp., normal), then $T$ is quasi-normal (resp.,normal), (ii) if $T$ is a contraction with ker $T=$ ker $T^{2}$ and $\tT$ is a partialisometry, then $T$ is a quasinormal partial isometry, and (iii) we show that if either(a) $T$ is a $w$-hyponormal operator such that $\n(T)\subset\n(T^*)$ and $S^*$ is $w$-hyponormal operator such that $\n(S^*)\subset \n(S)$or (b) $T$ is an invertible  $w$-hyponormal operator  and $S^*$ is $w$-hyponormal operator or (c) $T$ is a $w$-hyponormal such that $\n(T)\subset\n(T^*)$ and $S^*$ is a class $\Y$, then the pair $(T,S)$ satisfy Fuglede-Putnam property.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|