Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Weak amenability of triangular Banach algebras
HTML articles powered by AMS MathViewer

by B. E. Forrest and L. W. Marcoux PDF
Trans. Amer. Math. Soc. 354 (2002), 1435-1452 Request permission

Abstract:

Let $\mathcal {A}$ and $\mathcal {B}$ be unital Banach algebras, and let $\mathcal {M}$ be a Banach $\mathcal {A},\mathcal {B}$-module. Then $\mathcal {T} = \begin {bmatrix}\mathcal {A} & \mathcal {M}\\ 0 & \mathcal {B} \end {bmatrix}$ becomes a triangular Banach algebra when equipped with the Banach space norm $\left \Vert \begin {bmatrix} a & m\\ 0 & b \end {bmatrix} \right \Vert = \Vert a \Vert _{\mathcal {A}} + \Vert m \Vert _{\mathcal {M}} + \Vert b \Vert _{\mathcal {B}}$. A Banach algebra $\mathcal {T}$ is said to be $n$-weakly amenable if all derivations from $\mathcal {T}$ into its $n^{\mathrm {th}}$ dual space $\mathcal {T}^{(n)}$ are inner. In this paper we investigate Arens regularity and $n$-weak amenability of a triangular Banach algebra $\mathcal {T}$ in relation to that of the algebras $\mathcal {A}$, $\mathcal {B}$ and their action on the module $\mathcal {M}$.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46H25, 16E40
  • Retrieve articles in all journals with MSC (2000): 46H25, 16E40
Additional Information
  • B. E. Forrest
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • Email: beforres@math.uwaterloo.ca
  • L. W. Marcoux
  • Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • Address at time of publication: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • MR Author ID: 288388
  • Email: L.Marcoux@ualberta.ca, LWMarcoux@math.uwaterloo.ca
  • Received by editor(s): October 9, 1998
  • Received by editor(s) in revised form: July 20, 1999
  • Published electronically: December 4, 2001
  • Additional Notes: Research supported in part by NSERC (Canada)
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 354 (2002), 1435-1452
  • MSC (2000): Primary 46H25, 16E40
  • DOI: https://doi.org/10.1090/S0002-9947-01-02957-9
  • MathSciNet review: 1873013