Fredholm and Local Spectral Theory, with Applications to Multipliers

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Springer Science & Business Media, Feb 29, 2004 - Mathematics - 444 pages
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A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.
 

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Contents

II
1
III
2
IV
7
V
11
VI
14
VII
24
VIII
33
IX
43
XXXII
218
XXXIII
225
XXXIV
233
XXXV
239
XXXVI
240
XXXVII
244
XXXVIII
249
XXXIX
255

X
48
XI
55
XII
56
XIII
69
XIV
76
XV
90
XVI
99
XVII
109
XVIII
110
XIX
119
XX
127
XXI
132
XXII
143
XXIII
146
XXIV
157
XXV
164
XXVI
179
XXVII
182
XXVIII
191
XXIX
192
XXX
200
XXXI
210
XL
264
XLI
271
XLII
279
XLIII
286
XLIV
292
XLV
298
XLVI
309
XLVII
310
XLVIII
314
XLIX
323
L
331
LI
338
LII
357
LIII
361
LIV
367
LV
368
LVI
388
LVII
401
LVIII
415
LIX
423
LX
437
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Page 423 - On a commutative extension of a Banach algebra, Proc. Amer. Math. Soc. 13 (1962X 815-822.
Page 425 - Topics in harmonic analysis. Lecture notes, Department of Mathematics, Yale University, New Haven, 1969.

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