On (Co)homology of triangular Banach algebras
Tom 67 / 2005
Banach Center Publications 67 (2005), 271-276
MSC: Primary 46H25; Secondary 46M18, 16E40.
DOI: 10.4064/bc67-0-22
Streszczenie
Suppose that $A$ and $B$ are unital Banach algebras with units $1_A$ and $1_B$, respectively, $M$ is a unital Banach $A,B$-module, ${\cal T}= \left [{A\quad M\atop 0\quad B}\right]$ is the triangular Banach algebra, $X$ is a unital ${\cal T}$-bimodule, $X_{AA}=1_AX1_A$, $X_{BB}=1_BX1_B$, $X_{AB}=1_AX1_B$ and $X_{BA}=1_BX1_A$. Applying two nice long exact sequences related to $A$, $B$, ${\cal T}$, $X$, $X_{AA}$, $X_{BB}$, $X_{AB}$ and $X_{BA}$ we establish some results on (co)homology of triangular Banach algebras.
