**Contemporary Mathematics**

Volume: 328;
2003;
322 pp;
Softcover

MSC: Primary 32; 46; 47; 54;

**Print ISBN: 978-0-8218-3269-1
Product Code: CONM/328**

List Price: $98.00

AMS Member Price: $78.40

MAA Member Price: $88.20

**Electronic ISBN: 978-0-8218-7918-4
Product Code: CONM/328.E**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

# Function Spaces

Share this page *Edited by *
*Krzysztof Jarosz*

This volume presents papers from the Fourth Conference on Function
Spaces. The conference brought together mathematicians interested in various
problems within the general area of function spaces, allowing for discussion
and exchange of ideas on those problems and related questions.

The lectures covered a broad range of topics, including spaces and algebras
of analytic functions of one and of many variables (and operators on such
spaces), \(L^p\)-spaces, spaces of Banach-valued functions, isometries
of function spaces, geometry of Banach spaces, and related subjects.

Included are 26 articles written by leading experts. Known results, open
problems, and new discoveries are featured. Most papers are written for
nonexperts, so the book can serve as a good introduction to the material
presented.

#### Readership

Graduate students and research mathematicians interested in functional analysis.

# Table of Contents

## Function Spaces

- Contents iii4 free
- Preface v6 free
- Components of resolvent sets and local spectral theory 18 free
- The Fejér-Riesz inequality and the index of the shift 1522
- A Cauchy-Green formula on the unit sphere in C2 2128
- On α-dual algebras 3138
- A connected metric space that is not separably connected 3946
- Weighted Chebyshev centres and intersection properties of balls in Banach spaces 4350
- The boundary of the unit ball in H1-type spaces 5966
- Complete isometries - an illustration of noncommutative functional analysis 8592
- Some recent trends and advances in certain lattice ordered algebras 99106
- 1. Introduction 100107
- 2. Definitions and elementary properties 101108
- 3. l-algebra multiplications in C (X) 105112
- 4. Multiplication by an element as an operator 106113
- 5. Uniform completion and Dedekind completion 107114
- 6. Powers in l-algebras 108115
- 7. Functional Calculus on ƒ-algebras 111118
- 8. Relationships between l-algebra multiplications 113120
- 9. Connection between algebra and Riesz homomorphisms 115122
- 10. Positive derivations 118125
- 11. Cauchy-Schwarz inequalities 119126
- 12. Order biduals 120127
- 13. Ideal theory 122129
- 14. Representation of ƒ-algebras 124131
- 15. Linear biseparating maps on ƒ-algebras 127134
- References 130137

- An extension of a theorem of Wermer, Bernard, Sidney and Hatori to algebras of functions on locally compact spaces 135142
- Some mapping properties of p-summing operators with Hilbertian domain 145152
- The unique decomposition property and the Banach-Stone theorem 151158
- A survey of algebraic extensions of commutative, unital normed algebras 157164
- Some more examples of subsets of c0 and L1 [0, 1] failing the fixed point property 171178
- Homotopic composition operators on H∞ ( Bn) 177184
- Characterization of conditional expectation in terms of positive projections 189196
- The Krull nature of locally C*-algebras 195202
- Characterizations and automatic linearity for ring homomorphisms on algebras of functions 201208
- Carleson embeddings for weighted Bergman spaces 217224
- Weak* -extreme points of injective tensor product spaces 231238
- Determining sets and fixed points for holomorphic endomorphisms 239246
- Localization in the spectral theory of operators on Banach spaces 247254
- Abstract harmonic analysis, homological algebra, and operator spaces 263270
- Relative tensor products for modules over von Neumann algebras 275282
- Uniform algebras generated by unimodular functions 293300
- Analytic functions on compact groups and their applications to almost periodic functions 299306
- I. Analytic Functions on Groups 299306
- II. Shift Invariant Algebras on Groups 303310
- 1. Radó's and Riemann's theorems for analytic functions on groups 303310
- 2. Extension of linear multiplicative functionals of shift invariant algebras on groups 304311
- 3. Automorphisms of shift invariant algebras on groups 307314
- 4. Primary ideals of algebras of analytic functions on solenoidal groups 308315
- 5. Asymptotic almost periodic functions 309316

- III. Inductive limits and Shift Invariant Algebras on Solenoidal Groups 310317
- 1. Inductive limits of disc algebras on G-discs 310317
- 2. Inductive limits of algebras on subsets of G-discs 312319
- 3. Gleason parts of inductive limits of disc algebras on G-discs 314321
- 4. Inductive limits of H∞ spaces on G-discs 315322
- 5. H∞ spaces on solenoidal groups 316323
- 6. Bourgain algebras and inductive limits of algebras 318325