Quadratic Integrals and Factorization of Linear Operators | Zendy

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Quadratic Integrals and Factorization of Linear Operators

Author(s) -

Blower Gordon

Publication year - 1997

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610797005516

Subject(s) - mathematics , bounded function , linear operators , bounded operator , finite rank operator , operator (biology) , factorization , operator theory , pure mathematics , compact operator , linear map , quadratic equation , banach space , unit (ring theory) , algebra over a field , matrix (chemical analysis) , mathematical analysis , computer science , algorithm , extension (predicate logic) , biochemistry , chemistry , materials science , geometry , mathematics education , repressor , composite material , transcription factor , gene , programming language

We consider operators on the matrix‐valued disc algebra. We show that any bounded linear operator T : A ⊗ ¯ K → X to a Banach space X of cotype 2 induces a bounded operator G ν → X defined on some weighted Bergman space G ν on the unit disc. We give sufficient conditions on the weight ν for the formal inclusion A ⊗ ¯ K → G vto be 2− C *‐summing. Decompositions of T with respect to operator‐valued measures are obtained.

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