Spiros Argyros's Books

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

By: Spiros Argyros,Michael Lambrou,William Ellison Longstaff

Write a review Read reviews Take a Quiz Solve Book Puzzle

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

By: Spiros Argyros,Michael Lambrou,William Ellison Longstaff

Those families of (closed) subspaces of a (real or complex) Banach space that arise as the set of atoms of an atomic Boolean algebra subspace lattice, abbreviated ABSL, are characterized. This characterization is used to obtain new examples of ABSL's including some with one-dimensional atoms. ABSL's with one-dimensional atoms arise precisely from strong [italic capital]M-bases. The strong rank one density problem for ABSL's is discussed and some affirmative results are presented. Several new areas of investigation in the theory of ABSL's are uncovered.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

102

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821825119

ISBN 13

9780821825112

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

By: Spiros Argyros,Andreas Tolias

Write a review Read reviews Take a Quiz Solve Book Puzzle

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

By: Spiros Argyros,Andreas Tolias

A general method producing Hereditarily Indecomposable (H I) Banach spaces is provided. We apply this method to construct a nonseparable H I Banach space $Y$. This space is the dual, as well as the second dual, of a separable H I Banach space.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

128

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821835211

ISBN 13

9780821835210

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

This book contains two sets of notes prepared for the Advanced Course on R- sey Methods in Analysis given at the Centre de Recerca Matem` atica in January 2004, as part of its year-long research programme on Set Theory and its Appli- tions. The common goal of the two sets of notes is to help young mathematicians enter a very active area of research lying on the borderline between analysis and combinatorics. The solution of the distortion problem for the Hilbert space, the unconditional basic sequence problem for Banach spaces, and the Banach ho- geneous space problem are samples of the most important recent advances in this area, and our two sets of notes will give some account of this. But our main goal was to try to expose the general principles and methods that lie hidden behind and are most likely useful for further developments. The goal of the ?rst set of notes is to describe a general method of building norms with desired properties, a method that is clearly relevant when testing any sort of intuition about the in?nite-dimensional geometry of Banach spaces. The goal of the second set of notes is to expose Ramsey-theoretic methods relevant for describing the rough structure present in this sort of geometry. We would like to thank the coordinator of the Advanced Course, Joan Ba- ria, and the director of the CRM, Manuel Castellet, for giving us this challenging but rewarding opportunity. Part A SaturatedandConditional StructuresinBanachSpaces SpirosA.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

258

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764373601

ISBN 13

9783764373603

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ramsey Methods in Analysis

By: Spiros A. Argyros,Stevo Todorcevic

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

258

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764373601

ISBN 13

9783764373603

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

By: Spiros Argyros,Michael Lambrou,William Ellison Longstaff

Write a review Read reviews Take a Quiz Solve Book Puzzle

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

By: Spiros Argyros,Michael Lambrou,William Ellison Longstaff

This book provides a bridge between the theory of bases of Banach spaces and the study of certain types (reflexive, non-self-adjoint) of operator algebras, offering a viewpoint common to both areas. The authors give a characterization of those families of sub-spaces of a Banach space that arise as the set of atoms of an atomic Boolean subspace lattice (ABSL). They obtain new examples of ABSLs, including some with one-dimensional atoms. The latter are shown to arise precisely from strong M-bases of the underlying space. The authors also discuss, for any given ABSL, the question of the strong-operator density of the sub-algebra of finite-rank operators in the algebra of all operators leaving every atom invariant; some affirmative results are presented. On a separable Hilbert space, the given ABSL satisfies this density property if and only if a certain extremely non-commutative "factor" of it does. In addition, several other areas of investigation in the theory of ABSLs are considered, including "selection" from atoms, "slicing" of atoms, and the double commutant property. The authors also provide many examples.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

110

Publisher

American Mathematical Soc.

ISBN 10

0821861689

ISBN 13

9780821861684

Ramsey Methods in Analysis

By: Spiros Argyros,Stevo Todorcevic

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ramsey Methods in Analysis

By: Spiros Argyros,Stevo Todorcevic

We also apply the Nash-Williams theory of fronts and barriers in the study of Cezaro summability and unconditionality present in basic sequences inside a given Banach space. We further provide a detailed exposition of the block-Ramsey theory and its recent deep adjustments relevant to the Banach space theory due to Gowers."--BOOK JACKET.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

257

Publisher

Birkhauser

Published Date

ISBN 10

0817672648

ISBN 13

9780817672645

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

By: Spiros Argyros Andreas Tolias

Write a review Read reviews Take a Quiz Solve Book Puzzle

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

By: Spiros Argyros Andreas Tolias

A general method producing Hereditarily Indecomposable (H.I.) Banach spaces is provided. We apply this method to construct a nonseparable H.I. Banach space $Y$. This space is the dual, as well as the second dual, of a separable H.I. Banach space. Moreover the space of bounded linear operators ${\mathcal{L}}Y$ consists of elements of the form $\lambda I+W$ where $W$ is a weakly compact operator and hence it has separable range. Another consequence of the exhibited method is the proof of the complete dichotomy for quotients of H.I. Banach spaces. Namely we show that every separable Banach space $Z$ not containing an isomorphic copy of $\ell^1$ is a quotient of a separable H.I. space $X$. Furthermore the isomorph of $Z^*$ into $X^*$, defined by the conjugate operator of the quotient map, is a complemented subspace of $X^*$.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

132

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821865285

ISBN 13

9780821865286

Book's by Spiros Argyros

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

Atomic Boolean Subspace Lattices and Applications to the Theory of Bases

Ramsey Methods in Analysis

Ramsey Methods in Analysis

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

Methods in the Theory of Hereditarily Indecomposable Banach Spaces

Username

Password

Username

Password

Password again

Birthday

Email