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Tensor Products and Independent Sums of $\mathcal L_p$Spaces, $1 < p < \infty$
eBook ISBN:  9781470402495 
Product Code:  MEMO/138/660.E 
List Price:  $48.00 
MAA Member Price:  $43.20 
AMS Member Price:  $28.80 
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Tensor Products and Independent Sums of $\mathcal L_p$Spaces, $1 < p < \infty$
eBook ISBN:  9781470402495 
Product Code:  MEMO/138/660.E 
List Price:  $48.00 
MAA Member Price:  $43.20 
AMS Member Price:  $28.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 138; 1999; 77 ppMSC: Primary 46
Two methods of constructing infinitely many isomorphically distinct \(\mathcal L_p\)spaces have been published. In this volume, the author shows that these constructions yield very different spaces and in the process develop methods for dealing with these spaces from the isomorphic viewpoint.
ReadershipGraduate students and research mathematicians working in functional analysis.

Table of Contents

Chapters

0. Introduction

1. The constructions of $\mathcal {L}_p$spaces

2. Isomorphic properties of $(p, 2)$sums and the spaces $R^\alpha _p$

3. Isomorphic classification of $R^\alpha _p$, $\alpha < \omega _1$

4. Isomorphism from $X_p \otimes X_p$ into $(p, 2)$sums

5. Selection of bases in $X_p \otimes X_p$

6. $X_p \otimes X_p$preserving operators on $X_p \otimes X_p$

7. Isomorphisms of $X_p \otimes X_p$ onto complemented subspaces of $(p, 2)$sums

8. $X_p \otimes X_p$ is not in the scale $R^\alpha _p$, $\alpha < \omega _1$

9. Final remarks and open problems


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Volume: 138; 1999; 77 pp
MSC: Primary 46
Two methods of constructing infinitely many isomorphically distinct \(\mathcal L_p\)spaces have been published. In this volume, the author shows that these constructions yield very different spaces and in the process develop methods for dealing with these spaces from the isomorphic viewpoint.
Readership
Graduate students and research mathematicians working in functional analysis.

Chapters

0. Introduction

1. The constructions of $\mathcal {L}_p$spaces

2. Isomorphic properties of $(p, 2)$sums and the spaces $R^\alpha _p$

3. Isomorphic classification of $R^\alpha _p$, $\alpha < \omega _1$

4. Isomorphism from $X_p \otimes X_p$ into $(p, 2)$sums

5. Selection of bases in $X_p \otimes X_p$

6. $X_p \otimes X_p$preserving operators on $X_p \otimes X_p$

7. Isomorphisms of $X_p \otimes X_p$ onto complemented subspaces of $(p, 2)$sums

8. $X_p \otimes X_p$ is not in the scale $R^\alpha _p$, $\alpha < \omega _1$

9. Final remarks and open problems
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