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Tensor Products and Independent Sums of $$\mathcal L_p$$-Spaces, $$1 < p < \infty$$
Dale E. Alspach, Oklahoma State University, Stillwater, OK
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Memoirs of the American Mathematical Society
1999; 77 pp; softcover
Volume: 138
ISBN-10: 0-8218-0961-X
ISBN-13: 978-0-8218-0961-7
List Price: US$45 Individual Members: US$27
Institutional Members: US\$36
Order Code: MEMO/138/660

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.

Graduate students and research mathematicians working in functional analysis.

• Introduction
• The constructions of $$\mathcal L_p$$-spaces
• Isomorphic properties of $$(p,2)$$--sums and the spaces $$R^\alpha_p$$
• The isomorphic classification of $$R^\alpha_p$$, $$\alpha < \omega_1$$
• Isomorphisms from $$X_p\otimes X_p$$ into $$(p,2)$$--sums
• Selection of bases in $$X_p\otimes X_p$$
• $$X_p\otimes X_p$$-preserving operators on $$X_p\otimes X_p$$
• Isomorphisms of $$X_p\otimes X_p$$ onto complemented subspaces of $$(p,2)$$--sums
• $$X_p\otimes X_p$$ is not in the scale $$R^\alpha_p$$, $$\alpha < \omega_1$$
• Final remarks and open problems
• Bibliography