Gleason's problem and Schur multipliers in the multivariable quaternionic setting

被引：8

作者：

Abu-Ghanem, Khaled ^{[1
]}

Alpay, Daniel ^{[1
]}

Colombo, Fabrizio ^{[2
]}

Sabadini, Irene ^{[2
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 425卷 / 02期

关键词：

Several quaternionic variables; Gleason's problem; Schur multipliers; Realizations; Quaternionic Drury-Arveson; SLICE REGULAR FUNCTIONS; HILBERT-SPACES; INTERPOLATION; OPERATORS; ALGEBRAS; THEOREM;

D O I：

10.1016/j.jmaa.2015.01.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define and study the counterparts of Gleason's problem, of the Drury-Arveson's space and of Schur multipliers when the unit ball of C-N is replaced by the unit ball of H-N, where H denotes the algebra of real quaternions. Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. Finally, we define the counterpart of Blaschke factors in this setting and study a one point interpolation problem. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1083 / 1096

页数：14

共 27 条

[1] On commuting operators solving Gleason's problem [J].

Alpay, D ;

Dubi, C .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (11) :3285-3293

[2] Rational hyperholomorphic functions in R4 [J].

Alpay, D ;

Shapiro, M ;

Volok, D .

JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 221 (01) :122-149

[3] Reproducing kernel quaternionic pontryagin spaces [J].

Alpay, D ;

Shapiro, M .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2004, 50 (04) :431-476

[4] A theorem of Beurling-Lax type for Hilbert spaces of functions analytic in the unit ball [J].

Alpay, D ;

Dijksma, A ;

Rovnyak, J .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2003, 47 (03) :251-274

[5] Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem [J].

Alpay, D ;

Kaptanoglu, HT .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2002, 42 (01) :1-21

[6] Krein-Langer Factorization and Related Topics in the Slice Hyperholomorphic Setting [J].

Alpay, Daniel ;

Colombo, Fabrizio ;

Sabadini, Irene .

JOURNAL OF GEOMETRIC ANALYSIS, 2014, 24 (02) :843-872

[7] PONTRYAGIN-DE BRANGES-ROVNYAK SPACES OF SLICE HYPERHOLOMORPHIC FUNCTIONS [J].

Alpay, Daniel ;

Colombo, Fabrizio ;

Sabadini, Irene .

JOURNAL D ANALYSE MATHEMATIQUE, 2013, 121 :87-125

[8] Quaternionic Hilbert spaces and a von Neumann inequality [J].

Alpay, Daniel ;

Kaptanoglu, H. Turgay .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2012, 57 (06) :667-675

[9] Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting [J].

Alpay, Daniel ;

Colombo, Fabrizio ;

Sabadini, Irene .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2012, 72 (02) :253-289

[10]

Alpay Daniel, 1997, Operator Theory: Advances and Applications, V96, DOI DOI 10.1007/978-3-0348-8908-7

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