Spectral synthesis for A(G) and subspaces of VN(G)

被引：33

作者：

Kaniuth, E ^{[1
]}

Lau, AT

机构：

[1] Univ Gesamthsch Paderborn, Fachbereich Math Informat, D-33095 Paderborn, Germany

[2] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 2G1, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 11期

关键词：

D O I：

10.1090/S0002-9939-01-05924-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let G be a locally compact group, A(G) the Fourier algebra of G and VN(G) the von Neumann algebra generated by the left regular representation of G. We introduce the notion of X-spectral set and X-Ditkin set when X is an A(G)-invariant linear subspace of VN(G), thus providing a unified approach to both spectral and Ditkin sets and their local variants. Among other things, we prove results on unions of X-spectral sets and X-Ditkin sets, and an injection theorem for X-spectral sets.

引用

页码：3253 / 3263

页数：11

共 21 条

[1]

[Anonymous], 1972, MEM AM MATH SOC

[2] UNION OF SETS OF SYNTHESIS AND DITKINS CONDITION IN REGULAR BANACH-ALGEBRAS [J].

ATZMON, A .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1980, 2 (02) :317-320

[3] Weak*-closedness of subspaces of Fourier-Stieltjes algebras and weak*-continuity of the restriction map [J].

Bekka, MB ;

Kaniuth, E ;

Lau, AT ;

Schlichting, G .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 350 (06) :2277-2296

[4]

Benedetto J. J., 1975, SPECTRAL SYNTHESIS

[5] ALMOST PERIODIC OPERATORS IN VN(G) [J].

CHOU, C .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 317 (01) :229-253

[6] DITKIN SETS ON LOCALLY COMPACT-GROUPS [J].

DERIGHETTI, A .

MONATSHEFTE FUR MATHEMATIK, 1986, 101 (02) :95-113

[7]

Dunford N., 1958, LINEAR OPERATORS, VI

[8]

Eymard P., 1964, Bull. Soc. Math. Fr, V92, P181, DOI [DOI 10.24033/BSMF.1607, 10.24033/bsmf.1607]

[9] Fourier analysis on coset spaces [J].

Forrest, B .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1998, 28 (01) :173-190

[10]

GRANIRER EE, 1974, T AM MATH SOC, V189, P372

← 1 2 3 →