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Two dimensional commutative Banach algebras and von Neumann inequality

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83674

Title: Two dimensional commutative Banach algebras and von Neumann inequality
Authors: Nakazi, T. Browse this author
Yamamoto, t. Browse this author
Keywords: commutative Banach algebra
Q-algebra
two dimension
norm
von Neumann in­equality
Schwarz lemma
Issue Date: Jun-2001
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 528
Start Page: 1
End Page: 18
Abstract: We show the following: Let T3 be a two dimensional commutative Banach algebra with identity. If T3 satisfies TE B, \IT\I :'S 1 􀀉 \\f(T)I\ :'S 1 whenever f is a polynomial satisfying \f(z)\ :::; 1 (\z\ :'S 1) then T3 is isometric to a subalge­bra of the algebra B(H) of all bounded linear operators on some Hilbert space H, and T3 satisfies Tk E !3, IITklJ :'S 1 (k = 1, ... , n) 􀀉 llf(T1, ... , Tn) II :'S 1 whenever f is a polynomial inn variables satisfying lf(z1, ... , Zn)I :'S 1 (\zki :'S 1, k = 1, ... , n), for all n.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69278
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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