Strongly amenable involutive representations of involutive Banach algebras |
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Authors: | Fatemeh Akhtari Rasoul Nasr-Isfahani |
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Institution: | 1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111?, Isfahan, Iran 2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
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Abstract: | Let \(\mathfrak{A }\) be a Banach \(*\) -algebra and let \(\varphi \) be a nonzero self-adjoint character on \(\mathfrak{A }\) . For a \(*\) -representation \(\pi \) of \(\mathfrak{A }\) on a Hilbert space \(\mathcal{H }\) , we introduce and study strong \(\varphi \) -amenability of \(\pi \) in terms of certain states on the von Neumann algebra of bounded operators on \(\mathcal{H }\) . We then give some characterizations of this notion in terms of certain positive functionals on \(\mathfrak{A }\) . We finally investigate some hereditary properties of strong \(\varphi \) -amenability of Banach algebras. |
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