Similarities and differences between real and complex Banach spaces: an overview and recent developments

被引：13

作者：

Moslehian, M. S. ^{[1
]}

Munoz-Fernandez, G. A. ^{[2
]}

Peralta, A. M. ^{[3
]}

Seoane-Sepulveda, J. B. ^{[2
]}

机构：

[1] Ferdowsi Univ Mashhad, Ctr Excellence Anal Algebra Struct CEAAS, Dept Pure Math, POB 1159, Mashhad 91775, Razavi Khorasan, Iran

[2] Univ Complutense Madrid, Fac Ciencias Matemat, Inst Matemat Interdisciplinar IMI, Dept Anal Matemat & Matemat Aplicada, Plaza Ciencias 3, Madrid 28040, Spain

[3] Univ Granada, Inst Matemat, Dept Anal Matemat, Univ Granada IMAG,Fac Ciencias, Granada 18071, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2022年 / 116卷 / 02期

关键词：

Complexification; Banach space; Hilbert space; Polynomial; Operator algebra; BOHNENBLUST-HILLE INEQUALITY; C-STAR-ALGEBRAS; MULTIPLICATIVE LINEAR FUNCTIONALS; INVARIANT SUBSPACE PROBLEM; PHELPS-BOLLOBAS THEOREM; KAHANE-ZELAZKO THEOREM; LOWER BOUNDS; CONTRACTIVE PROJECTIONS; POLARIZATION CONSTANTS; ANALYTIC-FUNCTIONS;

D O I：

10.1007/s13398-022-01222-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There are numerous cases of discrepancies between results obtained in the setting of real Banach spaces and those obtained in the complex context. This article is a modern exposition of the subtle differences between key results and theories for complex and real Banach spaces and the corresponding linear operators between them. We deeply discuss some aspects of the complexification of real Banach spaces and give several examples showing how drastically different can be the behavior of real Banach spaces versus their complex counterparts.

引用

页数：80

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