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Spectral well-behaved *-representations

S. J. Bhatt, M. Fragoulopoulou, A. Inoue (2005)

Banach Center Publications

In this brief account we present the way of obtaining unbounded *-representations in terms of the so-called "unbounded" C*-seminorms. Among such *-representations we pick up a special class with "good behaviour" and characterize them through some properties of the Pták function.

Spectrum of certain Banach algebras and ∂̅-problems

Linus Carlsson, Urban Cegrell, Anders Fällström (2007)

Annales Polonici Mathematici

We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

Zhiguo Hu (1998)

Studia Mathematica

Let A be a semisimple commutative regular tauberian Banach algebra with spectrum Σ A . In this paper, we study the norm spectra of elements of s p a n ¯ Σ A and present some applications. In particular, we characterize the discreteness of Σ A in terms of norm spectra. The algebra A is said to have property (S) if, for all φ ¯ Σ A 0 , φ has a nonempty norm spectrum. For a locally compact group G, let 2 d ( Ĝ ) denote the C*-algebra generated by left translation operators on L 2 ( G ) and G d denote the discrete group G. We prove that the Fourier...

Spectrum preserving linear mappings in Banach algebras

B. Aupetit, H. du T. Mouton (1994)

Studia Mathematica

Let A and B be two unitary Banach algebras. We study linear mappings from A into B which preserve the polynomially convex hull of the spectrum. In particular, we give conditions under which such surjective linear mappings are Jordan morphisms.

Sphere equivalence, Property H, and Banach expanders

Qingjin Cheng (2016)

Studia Mathematica

We study the uniform classification of the unit spheres of general Banach sequence spaces. In particular, we obtain some interesting applications involving Property H introduced by Kasparov and Yu, and Banach expanders.

Spherical completeness with infinitesimals.

José Manuel Bayod (1982)

Revista Matemática Hispanoamericana

In the theory of nonarchimedean normed spaces over valued fields other than R or C, the property of spherical completeness is of utmost importance in several contexts, and it appears to play the role conventional completeness does in some topics of classical functional analysis. In this note we give various characterizations of spherical completeness for general ultrametric spaces, related to but different from the notions of pseudo-convergent sequence and pseudo-limit introduced by Ostrowski in...

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