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Hokkaido University Preprint Series in Mathematics >
Two dimensional commutative Banach algebras and von Neumann inequality
| 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 |
| Publisher: | Department of Mathematics, Hokkaido University |
| 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
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Submitter: 数学紀要登録作業用
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