ZERO JORDAN PRODUCT DETERMINED BANACH ALGEBRAS
Keyword(s):
A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if, for every Banach space $X$ , every bilinear map $\unicode[STIX]{x1D711}:A\times A\rightarrow X$ satisfying $\unicode[STIX]{x1D711}(a,b)=0$ whenever $a$ , $b\in A$ are such that $ab+ba=0$ , is of the form $\unicode[STIX]{x1D711}(a,b)=\unicode[STIX]{x1D70E}(ab+ba)$ for some continuous linear map $\unicode[STIX]{x1D70E}$ . We show that all $C^{\ast }$ -algebras and all group algebras $L^{1}(G)$ of amenable locally compact groups have this property and also discuss some applications.
2007 ◽
Vol 76
(1)
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pp. 49-54
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2009 ◽
Vol 79
(2)
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pp. 319-325
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2011 ◽
Vol 84
(3)
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pp. 372-386
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2011 ◽
Vol 63
(1)
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pp. 123-135
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2012 ◽
Vol 86
(2)
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pp. 315-321
1979 ◽
Vol 31
(1)
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pp. 53-67
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1985 ◽
Vol 95
(3)
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pp. 375-375
2010 ◽
Vol 258
(2)
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pp. 357-372
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