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An extremal problem in Banach algebras

100%

Olofsson A.

Studia Mathematica

2001

tom 145

nr 3

255-264

We study asymptotics of a class of extremal problems rₙ(A,ε) related to norm controlled inversion in Banach algebras. In a general setting we prove estimates that can be considered as quantitative refinements of a theorem of Jan-Erik Björk [1]. In the last section we specialize further and consider a class of analytic Beurling algebras. In particular, a question raised by Jan-Erik Björk in [1] is answered in the negative.

Operator-valued n-harmonic measure in the polydisc

100%

Olofsson A.

Studia Mathematica

2004

tom 163

nr 3

203-216

An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon an earlier result proved by R. E. Curto and F.-H. Vasilescu in [3].

Ograniczanie wyników

2 Studia Mathematica

2 Olofsson A.

1 2004

1 2001

Wyniki wyszukiwania

An extremal problem in Banach algebras

Operator-valued n-harmonic measure in the polydisc