Banach Embedding Properties of Non-Commutative Lp-Spaces (Memoirs of the American Mathematical Society)

U. Haagerup; H. P. Rosenthal; F. A. Sukochev

Published by American Mathematical Society, 2003
ISBN 10: 0821832719 / ISBN 13: 9780821832714
Used / Mass Market Paperback / Quantity Available: 0
Available From More Booksellers
View all  copies of this book

About the Book

We're sorry; this specific copy is no longer available. AbeBooks has millions of books. We've listed similar copies below.

Description:

Brand new. We distribute directly for the publisher. Let $\mathcal N$ and $\mathcal M$ be von Neumann algebras. It is proved that $L^p(\mathcal N)$ does not linearly topologically embed in $L^p(\mathcal M)$ for $\mathcal N$ infinite, $\mathcal M$ finite, $1\le p<2$. The following considerably stronger result is obtained (which implies this, since the Schatten $p$-class $C_p$ embeds in $L^p(\mathcal N)$ for $\mathcal N$ infinite).Theorem. Let $1\le p<2$ and let $X$ be a Banach space with a spanning set $(x_{ij})$ so that for some $C\ge 1$,(i) any row or column is $C$-equivalent to the usual $\ell^2$-basis,(ii) $(x_{i_k,j_k})$ is $C$-equivalent to the usual $\ell^p$-basis, for any $i_1\le i_2 \le\cdots$ and $j_1\le j_2\le \cdots$.Then $X$ is not isomorphic to a subspace of $L^p(\mathcal M)$, for $\mathcal M$ finite. Complements on the Banach space structure of non-commutative $L^p$-spaces are obtained, such as the $p$-Banach-Saks property and characterizations of subspaces of $L^p(\mathcal M)$ containing $\ell^p$ isomorphically. The spaces $L^p(\mathcal N)$ are classified up to Banach isomorphism (i.e., linear homeomorphism), for $\mathcal N$ infinite-dimensional, hyperfinite and semifinite, $1\le p<\infty$, $p\ne 2$. It is proved that there are exactly thirteen isomorphism types; the corresponding embedding properties are determined for $p<2$ via an eight level Hasse diagram. It is also proved for all $1\le p<\infty$ that $L^p(\mathcal N)$ is completely isomorphic to $L^p(\mathcal M)$ if $\mathcal N$ and $\mathcal M$ are the algebras associated to free groups, or if $\mathcal N$ and $\mathcal M$ are injective factors of type III$_\lambda$ and III$_{\lambda'}$ for $0<\lambda$, $\lambda'\le 1$. Bookseller Inventory #

About this title:

Book ratings provided by Goodreads:
0 avg rating
(0 ratings)

Synopsis: Let $\mathcal N$ and $\mathcal M$ be von Neumann algebras. It is proved that $L^p(\mathcal N)$ does not linearly topologically embed in $L^p(\mathcal M)$ for $\mathcal N$ infinite, $\mathcal M$ finite, $1\le p<2$. The following considerably stronger result is obtained (which implies this, since the Schatten $p$-class $C_p$ embeds in $L^p(\mathcal N)$ for $\mathcal N$ infinite). Theorem. Let $1\le p<2$ and let $X$ be a Banach space with a spanning set $(x_{ij})$ so that for some $C\ge 1$, (i) any row or column is $C$-equivalent to the usual $\ell^2$-basis, (ii) $(x_{i_k,j_k})$ is $C$-equivalent to the usual $\ell^p$-basis, for any $i_1\le i_2 \le\cdots$ and $j_1\le j_2\le \cdots$. Then $X$ is not isomorphic to a subspace of $L^p(\mathcal M)$, for $\mathcal M$ finite.Complements on the Banach space structure of non-commutative $L^p$-spaces are obtained, such as the $p$-Banach-Saks property and characterizations of subspaces of $L^p(\mathcal M)$ containing $\ell^p$ isomorphically. The spaces $L^p(\mathcal N)$ are classified up to Banach isomorphism (i.e., linear homeomorphism), for $\mathcal N$ infinite-dimensional, hyperfinite and semifinite, $1\le p<\infty$, $p\ne 2$. It is proved that there are exactly thirteen isomorphism types; the corresponding embedding properties are determined for $p<2$ via an eight level Hasse diagram. It is also proved for all $1\le p<\infty$ that $L^p(\mathcal N)$ is completely isomorphic to $L^p(\mathcal M)$ if $\mathcal N$ and $\mathcal M$ are the algebras associated to free groups, or if $\mathcal N$ and $\mathcal M$ are injective factors of type III$_\lambda$ and III$_{\lambda'}$ for $0<\lambda$, $\lambda'\le 1$.

"About this title" may belong to another edition of this title.

Bibliographic Details

Title: Banach Embedding Properties of ...
Publisher: American Mathematical Society
Publication Date: 2003
Binding: Mass Market Paperback
Book Condition: New

Top Search Results from the AbeBooks Marketplace

1.

Published by American Mathematical Society
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Paperback Quantity Available: 2
Seller:
THE SAINT BOOKSTORE
(Southport, United Kingdom)
Rating
[?]

Book Description American Mathematical Society. Paperback. Condition: New. New copy - Usually dispatched within 2 working days. Seller Inventory # B9780821832714

More information about this seller | Contact this seller

Buy New
US$ 52.75
Convert Currency

Add to Basket

Shipping: US$ 9.33
From United Kingdom to U.S.A.
Destination, Rates & Speeds

2.

U. Haagerup, H. P. Rosenthal, F. A. Sukochev
Published by American Mathematical Society, United States (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Paperback Quantity Available: 1
Seller:
The Book Depository
(London, United Kingdom)
Rating
[?]

Book Description American Mathematical Society, United States, 2003. Paperback. Condition: New. Language: English . Brand New Book. Let $ mathcal N$ and $ mathcal M$ be von Neumann algebras. It is proved that $L^p( mathcal N)$ does not linearly topologically embed in $L^p( mathcal M)$ for $ mathcal N$ infinite, $ mathcal M$ finite, $1 le p. Seller Inventory # AAN9780821832714

More information about this seller | Contact this seller

Buy New
US$ 56.56
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

3.

U. Haagerup
Published by American Mathematical Society (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Quantity Available: 2
Seller:
Books2Anywhere
(Fairford, GLOS, United Kingdom)
Rating
[?]

Book Description American Mathematical Society, 2003. PAP. Condition: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Seller Inventory # CE-9780821832714

More information about this seller | Contact this seller

Buy New
US$ 56.92
Convert Currency

Add to Basket

Shipping: US$ 12.10
From United Kingdom to U.S.A.
Destination, Rates & Speeds

4.

U. Haagerup, H. P. Rosenthal, F. A. Sukochev
Published by American Mathematical Society, United States (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Paperback Quantity Available: 1
Seller:
Book Depository International
(London, United Kingdom)
Rating
[?]

Book Description American Mathematical Society, United States, 2003. Paperback. Condition: New. Language: English . Brand New Book. Let $ mathcal N$ and $ mathcal M$ be von Neumann algebras. It is proved that $L^p( mathcal N)$ does not linearly topologically embed in $L^p( mathcal M)$ for $ mathcal N$ infinite, $ mathcal M$ finite, $1 le p. Seller Inventory # AAN9780821832714

More information about this seller | Contact this seller

Buy New
US$ 62.24
Convert Currency

Add to Basket

Shipping: FREE
From United Kingdom to U.S.A.
Destination, Rates & Speeds

5.

HAAGERUP ROSENTHAL SUKOCHEV
Published by American Mathematical Society (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Paperback Quantity Available: 1
Seller:
Herb Tandree Philosophy Books
(Stroud, GLOS, United Kingdom)
Rating
[?]

Book Description American Mathematical Society, 2003. Paperback. Condition: NEW. 9780821832714 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE01498024

More information about this seller | Contact this seller

Buy New
US$ 66.38
Convert Currency

Add to Basket

Shipping: US$ 10.75
From United Kingdom to U.S.A.
Destination, Rates & Speeds

6.

Haagerup, U./ Rosenthal, H. P./ Sukochev, F. A.
Published by Amer Mathematical Society (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Paperback Quantity Available: 2
Seller:
Revaluation Books
(Exeter, United Kingdom)
Rating
[?]

Book Description Amer Mathematical Society, 2003. Paperback. Condition: Brand New. illustrated edition edition. 65 pages. 9.75x7.00x0.25 inches. In Stock. Seller Inventory # __0821832719

More information about this seller | Contact this seller

Buy New
US$ 71.50
Convert Currency

Add to Basket

Shipping: US$ 8.06
From United Kingdom to U.S.A.
Destination, Rates & Speeds

7.

U. Haagerup, H. P. Rosenthal, F. A. Sukochev
Published by Amer Mathematical Society (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
New Mass Market Paperback Quantity Available: 1
Seller:
Ergodebooks
(RICHMOND, TX, U.S.A.)
Rating
[?]

Book Description Amer Mathematical Society, 2003. Mass Market Paperback. Condition: New. Seller Inventory # DADAX0821832719

More information about this seller | Contact this seller

Buy New
US$ 74.41
Convert Currency

Add to Basket

Shipping: US$ 4.99
Within U.S.A.
Destination, Rates & Speeds

8.

Haagerup, U., Rosenthal, H. P., Sukochev, F. A.
Published by Amer Mathematical Society (2003)
ISBN 10: 0821832719 ISBN 13: 9780821832714
Used Quantity Available: 1
Seller:
Better World Books Ltd
(Dunfermline, United Kingdom)
Rating
[?]

Book Description Amer Mathematical Society, 2003. Condition: Very Good. Ships from the UK. Great condition for a used book! Minimal wear. Seller Inventory # GRP97469889

More information about this seller | Contact this seller

Buy Used
US$ 96.86
Convert Currency

Add to Basket

Shipping: US$ 4.52
From United Kingdom to U.S.A.
Destination, Rates & Speeds