On completely hyperexpansive operators

被引：65
作者：
Athavale, A
机构：
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 124卷 / 12期
关键词：
positive definite; negative definite; completely monotone; completely alternating; subnormal; completely hyperexpansive;
D O I：
10.1090/S0002-9939-96-03609-X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce and discuss a class of operators, to be referred to as the class of completely hyperexpansive operators, which is in some sense antithetical to the class of contractive subnormals. The new class is intimately related to the theory of negative definite functions on abelian semigroups. The known interplay between positive and negative definite functions from the theory of harmonic analysis on semigroups can be exploited to reveal some interesting connections between subnormals and completely hyperexpansive operators.
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页码：3745 / 3752
页数：8
相关论文
共 10 条
[1]  
AGLER J, 1985, J OPERAT THEOR, V13, P203
[2]  
[Anonymous], HARMONIC ANAL SEMIGR
[3]   HOLOMORPHIC KERNELS AND COMMUTING OPERATORS [J].
ATHAVALE, A .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 304 (01) :101-110
[4]  
ATHAVALE A, 1991, P AM MATH SOC, V112, P701
[5]   POSITIVE DEFINITE FUNCTIONS ON ABELIAN SEMIGROUPS [J].
BERG, C ;
CHRISTENSEN, JPR ;
RESSEL, P .
MATHEMATISCHE ANNALEN, 1976, 223 (03) :253-274
[6]   SELFCOMMUTATORS OF MULTICYCLIC HYPONORMAL OPERATORS ARE ALWAYS TRACE CLASS [J].
BERGER, CA ;
SHAW, BI .
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (06) :1193-1199
[7]  
Conway J. B., 1991, The theory of subnormal operators
[8]   INVARIANT SUBSPACES OF THE DIRICHLET SHIFT [J].
RICHTER, S .
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1988, 386 :205-220
[9]  
Shields A., 1974, MATH SURVEYS, V13, P49
[10]   WHICH WEIGHTED SHIFTS ARE SUBNORMAL [J].
STAMPFLI, JG .
PACIFIC JOURNAL OF MATHEMATICS, 1966, 17 (02) :367-&
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