Weak amenability of triangular Banach algebras |
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| Authors: | B. E. Forrest L. W. Marcoux |
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| Affiliation: | Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 ; Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 |
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| Abstract: | Let  and  be unital Banach algebras, and let  be a Banach  -module. Then ![${mathcal T} = left[ begin{array}{cc} {mathcal A} & {mathcal M} 0 & {mathcal B} end{array} right]$](http://www.ams.org/tran/2002-354-04/S0002-9947-01-02957-9/gif-abstract0/img5.gif) becomes a triangular Banach algebra when equipped with the Banach space norm ![$ensuremath {Vert}left[ begin{array}{cc} a & m 0 & b end{array} right] ... ...rt} _{{mathcal M}} + ensuremath {Vert} b ensuremath {Vert} _{{mathcal B}}$](http://www.ams.org/tran/2002-354-04/S0002-9947-01-02957-9/gif-abstract0/img6.gif) . A Banach algebra  is said to be  -weakly amenable if all derivations from  into its  dual space  are inner. In this paper we investigate Arens regularity and  -weak amenability of a triangular Banach algebra  in relation to that of the algebras  ,  and their action on the module  . |
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