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Multidimensional weak resolvents and spatial equivalence of normal operators

100%

Jasiczak M.

Studia Mathematica

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2006

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tom 173

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nr 2

129-147

EN

The aim of this paper is to answer some questions concerning weak resolvents. Firstly, we investigate the domain of extension of weak resolvents Ω and find a formula linking Ω with the Taylor spectrum. We also show that equality of weak resolvents of operator tuples A and B results in isomorphism of the algebras generated by these operators. Although this isomorphism need not be of the form (1) X ↦ U*XU, where U is an isometry, for normal operators it is always possible to find a "large" subspace on which unitary similarity holds. This observation is used to prove that the infinite inflation of the spatial isomorphism between algebras generated by inflations of A and B, respectively, does have the form (1). These facts are generalized to other not necessarily commuting operators. We deal mostly with the self-adjoint case.

2

Extension from linear subvarieties for the Bergman scale of spaces on convex domains

100%

Jasiczak M.

Annales Polonici Mathematici

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2014

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tom 112

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nr 1

1-23

EN

We study the problem of extending functions from linear affine subvarieties for the Bergman scale of spaces on convex finite type domains. Our results solve the problem for H¹(D). For other Bergman spaces the result is ϵ-optimal.

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Universal divisors for Hardy spaces in the polydisk

100%

Jasiczak M.

Annales Polonici Mathematici

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2007

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tom 91

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nr 1

71-84

EN

We show that for an interpolating sequence in the polydisk one can construct a universal divisor for Hardy spaces.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Studia Mathematica

3 Jasiczak M.

1 2014

1 2007

1 2006

Multidimensional weak resolvents and spatial equivalence of normal operators

Extension from linear subvarieties for the Bergman scale of spaces on convex domains

Universal divisors for Hardy spaces in the polydisk