MODULE GENERALIZED DERIVATIONS ON TRIANGULAUR BANACH ALGEBRAS

- module. Applying the concept of module maps, (inner) module
generalized derivations and generalized first cohomology groups, we
present several results concerning the relations between module
generalized derivations from

A_{i}

into the dual space

A_{i}^{*}

(for

i = 1, 2

) and such derivations from the triangular Banach algebra
of the form

Misplaced &

into the associated triangular

m a t h c a l T

- bimodule

m a t h c a l T^{*}

of the
form

Misplaced &

. In particular, we show that the so-called generalized first
cohomology group from

m a t h c a l T

m a t h c a l T^{*}

is isomorphic to the directed sum of the generalized first
cohomology group from

A_{1}

A_{1}^{*}

and the generalized first
cohomology group from

A_{2}

A_{2}^{*}

Keywords

20.1001.1.22517952.2013.2.1.4.7

Volume 2, Issue 1 - Serial Number 1
August 2013
Pages 43-52

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History

Receive Date: 22 November 2013
Revise Date: 01 January 2014
Accept Date: 26 January 2014

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