TAILIEUCHUNG - Báo cáo toán học: "Invariant subspaces for subquasiscalar operators "

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Subspaces bất biến cho các nhà khai thác subquasiscalar. | J. OPERATOR THEORY 3 1980 159-164 Copyright by INCREST 1980 INVARIANT SUBSPACES FOR SUBQUASISCALAR OPERATORS CONSTANTIN APOSTOL Let z be a Banach space over the complex field c and let J5 Z denote the algebra of all bounded linear operators acting in z. Throughout this paper Se d Z will be a fixed quasiscalar operator . there exists a continuous linear multiplicative extension -T ơ S - jSf Z of the Riesz-Dunford functional calculus of s with analytic functions GS g .S denotes the supnorm algebra of all continuous complex functions defined on the spectrum of S . The symbol T will denote the restriction of s to an invariant subSpace X z. In other words T e ẫ Z will be a subquasiscalar operator having 5 e Sf Z as a quasiscalar extension. A rationally invariant subspace of T will mean a subspace in X invariant for Ấ T -1 V Ả ị ơ T and in particular an invariant subspace of T. We shall prove the following two theorems Theorem 1. T has a proper invariant subspace. Theorem 2. ỵ intơ 77 0 then T has a proper rationally invariant subspace. The above Theorem 1 is a Banach space variant of Scott Brown s Theorem 4 The proof of both theorems will be given at the end of the paper. Let G be a bounded open connected subset of c G A 0 and let L G L IG be the integrable resp. essentially bounded with respect to Lebesgue planar measure classes of complex functions on G. The weak topology of LXiG is the Z1 G -topo-logy. The subspace HV G c L G of all bounded analytic functions defined in G is w -closed and can be canonically identified with the dual of the separable Banach space M G L Gy Hx Gy- n L G see 11 4 . The weak topology of H G will be the M G -topology. For any Ẽ G the evaluation at p in H G will be denoted by By the part i of the proof of 11 Theorem we know that we have ển e M G . As in 11 4 we shall say that a subset Ơ of G is dominating in G if IIÍU sup 2 l V 6 77 G . Aeơ 160 CONSTANTIN APOSTOL Let US put tfcfrCS p supp p c G and for any fe Ha G pe dG ơ S define .

• Báo cáo khoa học
• báo cáo của tạp chí Journal of Operator Theory
• tài liệu báo cáo nghiện cứu khoa học
• cách trình bày báo cáo
• kiến thức toán học
• báo cáo toán học
• tài liệu báo cáo nghiên cứu khoa học