# Strongly amenable involutive representations of involutive Banach algebras

Strongly amenable involutive representations of involutive Banach algebras Let $$\mathfrak{A }$$ A be a Banach $$*$$ ∗ -algebra and let $$\varphi$$ φ be a nonzero self-adjoint character on $$\mathfrak{A }$$ A . For a   $$*$$ ∗ -representation $$\pi$$ π of $$\mathfrak{A }$$ A on a Hilbert space $$\mathcal{H }$$ H , we introduce and study strong $$\varphi$$ φ -amenability of $$\pi$$ π in terms of certain states on the von Neumann algebra of bounded operators on $$\mathcal{H }$$ H . We then give some characterizations of this notion in terms of certain positive functionals on $$\mathfrak{A }$$ A . We finally investigate some hereditary properties of strong $$\varphi$$ φ -amenability of Banach algebras. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Strongly amenable involutive representations of involutive Banach algebras

, Volume 18 (2) – Aug 9, 2013
18 pages

/lp/springer_journal/strongly-amenable-involutive-representations-of-involutive-banach-HLhnbgkWFX
Publisher
Springer Journals
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-013-0251-7
Publisher site
See Article on Publisher Site

### Abstract

Let $$\mathfrak{A }$$ A be a Banach $$*$$ ∗ -algebra and let $$\varphi$$ φ be a nonzero self-adjoint character on $$\mathfrak{A }$$ A . For a   $$*$$ ∗ -representation $$\pi$$ π of $$\mathfrak{A }$$ A on a Hilbert space $$\mathcal{H }$$ H , we introduce and study strong $$\varphi$$ φ -amenability of $$\pi$$ π in terms of certain states on the von Neumann algebra of bounded operators on $$\mathcal{H }$$ H . We then give some characterizations of this notion in terms of certain positive functionals on $$\mathfrak{A }$$ A . We finally investigate some hereditary properties of strong $$\varphi$$ φ -amenability of Banach algebras.

### Journal

PositivitySpringer Journals

Published: Aug 9, 2013

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