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# ðŸ“™ Methods in the Theory of Hereditarily Indecomposable Banach Spaces by S. Argyros, A. Tolias â€” epub download

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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 $X^*$.

## About book:

## About file:

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- Series:
**Memoirs of the American Mathematical Society** - Author:
**S. Argyros, A. Tolias** - Year:
**2004** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0821835211,9780821835210**

- File size:
**11 961 050** - Format:
**pdf**

Security code:

This book presents an overview of modern Banach space theory. It contains sixteen papers that reflect the wide expanse of the subject. Articles are gathered into five sections according to methodology rather than the topics considered. The sections are: g...

This book on Banach space theory focuses on what have been called three-space problems. It contains a fairly complete description of ideas, methods, results and counterexamples. It can be considered self-contained, beyond a course in functional analysis a...

In this Tract, Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Much of the presentation is based on research carried out over the last twenty-five years and has never appeared in...

In this Tract, Dr Ruston presents analogues for operators on Banach spaces of Fredholm's solution of integral equations of the second kind. Much of the presentation is based on research carried out over the last twenty-five years and has never appeared in...

Since its development by Leray and Schauder in the 1930's, degree theory in Banach spaces has proved to be an important tool in tackling many analytic problems, including boundary value problems in ordinary and partial differential equations, integral equ...

Since its development by Leray and Schauder in the 1930's, degree theory in Banach spaces has proved to be an important tool in tackling many analytic problems, including boundary value problems in ordinary and partial differential equations, integral equ...

Considering Poisson random measures as the driving sources for stochastic (partial) differential equations allows us to incorporate jumps and to model sudden, unexpected phenomena. By using such equations the present book introduces a new method for model...

Since its development by Leray and Schauder in the 1930's, degree theory in Banach spaces has proved to be an important tool in tackling many analytic problems, including boundary value problems in ordinary and partial differential equations, integral equ...

This short course on classical Banach space theory is a natural follow-up to a first course on functional analysis. The topics covered have proven useful in many contemporary research arenas, such as harmonic analysis, the theory of frames and wavelets, s...