Displaying similar documents to “Unitary Banach algebras”

Isometries of the unitary groups in C*-algebras

Osamu Hatori (2014)

Studia Mathematica

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We give a complete description of the structure of surjective isometries between the unitary groups of unital C*-algebras. While any surjective isometry between the unitary groups of von Neumann algebras can be extended to a real-linear Jordan *-isomorphism between the relevant von Neumann algebras, this is not the case for general unital C*-algebras. We show that the unitary groups of two C*-algebras are isomorphic as metric groups if and only if the C*-algebras are isomorphic in the...

Jucys-Murphy elements and the unitary Weingarten function

Jonathan I. Novak (2010)

Banach Center Publications

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We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.

Vector space isomorphisms of non-unital reduced Banach *-algebras

Rachid ElHarti, Mohamed Mabrouk (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras...

When is there a discontinuous homomorphism from L¹(G)?

Volker Runde (1994)

Studia Mathematica

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Let A be an A*-algebra with enveloping C*-algebra C*(A). We show that, under certain conditions, a homomorphism from C*(A) into a Banach algebra is continuous if and only if its restriction to A is continuous. We apply this result to the question in the title.

Dual Banach algebras: representations and injectivity

Matthew Daws (2007)

Studia Mathematica

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of...

On φ-inner amenable Banach algebras

A. Jabbari, T. Mehdi Abad, M. Zaman Abadi (2011)

Colloquium Mathematicae

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Generalizing the concept of inner amenability for Lau algebras, we define and study the notion of φ-inner amenability of any Banach algebra A, where φ is a homomorphism from A onto ℂ. Several characterizations of φ-inner amenable Banach algebras are given.