Operator-valued rational functions

被引：2

作者：

Curto, Raul E. ^{[1
]}

Hwang, In Sung ^{[2
]}

Lee, Woo Young ^{[3
,4
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Sungkyunkwan Univ, Dept Math, Suwon 16419, South Korea

[3] Seoul Natl Univ, Dept Math, RIM, Seoul 08826, South Korea

[4] Seoul Natl Univ, RIM, Seoul 08826, South Korea

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 283卷 / 09期

关键词：

Inner functions; Inner divisors; Blaschke-Potapov factor; Operator-valued rational functions; SUBNORMAL TOEPLITZ-OPERATORS;

D O I：

10.1016/j.jfa.2022.109640

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that every inner divisor of the operator-valued coordinate function, zI(E), is a Blaschke-Potapov factor. We also introduce a notion of operator-valued "rational " function and then show that delta is two-sided inner and rational if and only if it can be represented as a finite Blaschke-Potapov product; this extends to operator-valued functions the well-known result proved by V.P. Potapov for matrix-valued functions. (C) 2022 Elsevier Inc. All rights reserved.

引用

页数：23

共 50 条

[1] On operator-valued spherical functions
Stetkær, H
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 224 (02) : 338 - 351
[2] On Operator-valued Measurable Functions
Fourie, Jan H.
[J]. VECTOR MEASURES, INTEGRATION AND RELATED TOPICS, 2010, 201 : 205 - 214
[3] Operator-valued measurable functions
Bagheri-Bardi, G. A.
[J]. BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2015, 22 (01) : 159 - 163
[4] CONVEXITY OF OPERATOR-VALUED FUNCTIONS
HSU, IC
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (05): : A489 - A489
[5] Addition theorems for operator-valued functions
Ekaterina Shulman
[J]. Aequationes mathematicae, 2003, 66 (1-2) : 78 - 84
[6] GENERALIZED INVERSES OF OPERATOR-VALUED FUNCTIONS
LAY, DC
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (07): : A664 - A664
[7] INTEGRATION WITH RESPECT TO OPERATOR-VALUED FUNCTIONS
KRABBE, GL
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1961, 67 (02) : 214 - +
[8] SIMPLE POLES OF OPERATOR-VALUED FUNCTIONS
HOWLAND, JS
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1971, 36 (01) : 12 - &
[9] Remarks on Measurability of Operator-Valued Functions
Oscar Blasco
Ismael García-Bayona
[J]. Mediterranean Journal of Mathematics, 2016, 13 : 5147 - 5162
[10] A STOCHASTIC INTEGRAL FOR OPERATOR-VALUED FUNCTIONS
VAKHANIYA, NN
KANDELSK.NP
[J]. THEORY OF PROBILITY AND ITS APPLICATIONS,USSR, 1967, 12 (03): : 525 - +

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