The Fredholm index of a pair of commuting operators. II
type: Item
instance of: scholarly article
title: The Fredholm index of a pair of commuting operators. II
zbMATH Open document ID: 1166.47009
author: Xiang Fang
published in: Journal of Functional Analysis
publication date: 2009-04-08T00:00:00Z
review text: The author continues to study a method to calculate the Fredholm index of a pair of commuting operators [for Part~I, see Geom.\ Funct.\ Anal.\ 16, No.\,2, 367--402 (2006; Zbl 1105.47008)]. He shows first that an inequality obtained by \textit{R.\,G.\thinspace Douglas} and \textit{K.--R.\thinspace Yan} [Indiana Univ.\ Math.\ J.\ 42, No.\,3, 811--820 (1993; Zbl 0808.46068)] on Hilbert modules is actually equality. This result leads to a proof of the semi-continuity of the generalized Samuel multiplicities for a pair of commuting operators. As an application, it is shown that the Samuel additivity formula on Hilbert spaces of holomorphic functions is equivalent to a generalized Gleason problem, leading in turn to the additivity of Samuel multiplicity on the symmetric Fock space.
reviewed by: Florian-Horia Vasilescu
Mathematics Subject Classification ID: 47A13
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 5541656
zbMATH Keywords: multivariable operator theory
zbMATH Keywords: Fredholm index
zbMATH Keywords: Samuel multiplicity
zbMATH Keywords: a tuple of commuting operators
zbMATH Keywords: symmetric Fock space
MaRDI profile type: Publication
full work available at URL: j.jfa.2009.01.024
OpenAlex ID: W2094380234
cites work: \(m\)-isometric transformations of Hilbert space. I
cites work: Q4855416
cites work: The curvature invariant of a Hilbert module over ℂ [z1, ..., zd]
cites work: Q3995291
cites work: Complex geometry and operator theory
cites work: Generalized Bergman Kernels and the Cowen-Douglas Theory
cites work: Q4284563
cites work: Q3992983
cites work: Q4285026
cites work: Q4317713
cites work: On the Hilbert-Samuel multiplicity of Fredholm tuples
cites work: Samuel multiplicity and Fredholm theory
cites work: Q4846424
cites work: Hilbert polynomials and Arveson's curvature invariant.
cites work: Samuel multiplicity and the structure of semi-Fredholm operators
cites work: Invariant subspaces of the Dirichlet space and commutative algebra
cites work: The Fredholm index of quotient Hilbert modules
cites work: The Fredholm index of a pair of commuting operators
cites work: On the index of invariant subspaces in spaces of analytic functions of several complex variables
cites work: Q5515607
cites work: Q4143433
cites work: Q3483861
cites work: Analytic families of differential complexes
cites work: Q3683041
cites work: Base change and the Fredholm index
cites work: Spectral theory and sheaf theory. II
cites work: A Representation Theorem for Cyclic Analytic Two-Isometries
cites work: FREDHOLM COMPLEXES
cites work: A joint spectrum for several commuting operators
cites work: The analytic-functional calculus for several commuting operators
cites work: Q3958979
cites work: On two variable Jordan block. II
DOI: 10.1016/J.JFA.2009.01.024
description: scientific article; zbMATH DE number 5541656