$\sigma$-‎Intertwinings, ‎‎$\sigma$-‎Cocycles‎ and ‎Aotumatic ‎Continuity‎‎

Hussien Mahdavian Rad, Assadollah Niknam

Abstract


‎Let A be an ‎algebra and  X ‎an‎ A-bimodule ‎and‎ $‎\sigma$   a‎ ‎continuous ‎homomorphism on A. ‎‎‎‎In this ‎paper,‎ we show a ‎continuous‎ ‎linear ‎one ‎to ‎one ‎correspondence ‎ ‎ between  ‎the ‎set ‎of ‎all‎ module ‎valued ‎$‎\sigma‎$‎-‎‎‎derivations‎ ‎and ‎‎‎ the set of all ‎left $\sigma$‎-‎‎intertwining ‎mappings.  A‎‎ ‎similar ‎fact ‎is ‎proved‎ for ‎ ‎the ‎set ‎of ‎all‎ ‎‎n‎‎-‎‎$‎\sigma‎$‎-‎‎‎cocycles, where is a natural number.

‎Also ‎there ‎exists‎ a ‎linear homeomorphism between ‎‎‎ ‎the ‎set ‎of ‎all ‎continuous ‎‎module ‎valued ‎$‎\sigma‎$‎-‎derivations‎,‎ ‎and ‎‎B(A‎, X‎)‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎. ‎Moreove,‎‎ ‎it ‎is ‎proved that the same relation ‎satisfies‎ for ‎ ‎the ‎set ‎of ‎all‎ ‎‎n‎‎-‎‎$‎\sigma‎$‎-‎‎‎cocycles.


Refbacks

  • There are currently no refbacks.


Copyright 2019 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|