文档介绍：ü þ)ÛHilbert˜m4ŒØCf˜m Á‡
Á ‡
©ïÄü þS)Û Hilbert ˜m9 Dirichlet ˜m4ŒØCf˜m¯K.
Äky²
S)Û Hilbert ˜m4ŒØCf˜m•I•1. Ùgé˜aS)ÛHilbert˜
m•I•1ØCf˜mM, y²
M4ŒØCf˜mNäk/ªN = (z −λ)M. •
é Dirichlet ˜m4ŒØCf˜m‰Ñ
•x, = M • D 4ŒØCf˜m
…=M = [z −λ] = (z −λ)D, Ù¥λ∈ D.
'…cµS)Û Hilbert ˜m; k•{‘; •I; 4ŒØCf˜m; Dirichlet ˜m.
Š ö:Ü·
•“:¥Ô (Ç)
I
Abstract Maximal invariant subspaces for Hilbert spaces of analytic functions
Maximal invariant subspaces for Hilbert
spaces of analytic functions over the unit disc
Abstract
In this paper, we focus on maximal invariant subspaces for ordered analytic Hilbert
spaces over the unit disc and the Dirichlet space. Firstly, we show that maximal in-
variant subspaces in ordered analytic Hilbert spaces have index one. Secondly, we
obtain that if M is an invariant subspace of a class of ordered analytic Hilbert spaces
and dim M zM=1, then every maximal invariant subspace of M is of the form
N = (z −λ)M. Finally, we give plete description for maximal invariant sub-
spaces of the Dirichlet space. That is, an invariant subspace M of the Dirichlet space is
maximal if and only if M is of the form M = [z −λ] = (z −λ)D, λ∈ D.
Keywords: ordered analytic Hilbert spaces; finite codimension ; index ; maximal in-
variant subspace; Dirichlet space.
Written by Zhang Jing
Supervised by Prof. Wei Shuyun
II
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1˜Ù Úó . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1Ù S)ÛHilbert˜m4ŒØCf˜m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
1nÙ Dirichlet˜m4ŒØCf˜m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
ë•©z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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ü þ)ÛHilbert˜m4ŒØCf˜m 1˜