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# đź“™ Optimal Domain and Integral Extension of Operators: Acting in Function Spaces by Susumu Okada, Werner J. Ricker, Enrique A. SĂˇnchez PĂ©rez (auth.) â€” epub download

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Operator theory and functional analysis have a long tradition, initially being guided by problems from mathematical physics and applied mathematics. Much of the work in Banach spaces from the 1930s onwards resulted from investigating how much real (and complex) variable function theory might be extended to fu- tions taking values in (function) spaces or operators acting in them. Many of the ?rst ideas in geometry, basis theory and the isomorphic theory of Banach spaces have vector measure-theoretic origins and can be credited (amongst others) to N. Dunford, I.M. Gelfand, B.J. Pettis and R.S. Phillips. Somewhat later came the penetratingcontributionsofA.Grothendieck,whichhavepervadedandin?uenced theshapeoffunctionalanalysisandthetheoryofvectormeasures/integrationever since. Today, each of the areas of functional analysis/operator theory, Banach spaces, and vector measures/integration is a strong discipline in its own right. However, it is not always made clear that these areas grew up together as cousins and that they had, and still have, enormous in?uences on one another. One of the aims of this monograph is to reinforce and make transparent precisely this important point.

- Series:
**Operator Theory: Advances and Applications 180** - Author:
**Susumu Okada, Werner J. Ricker, Enrique A. SĂˇnchez PĂ©rez (auth.)** - Year:
**2008** - Publisher:
**BirkhĂ¤user Basel** - Language:
**English** - ISBN:
**978-3-7643-8647-4,978-3-7643-8648-1**

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**2 749 979** - Format:
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This volume of the "Mathematics Studies" series presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mat...

"Theory of Function Spaces II" deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales os spaces cover many well-known function spaces such as H?lder-Zygmund spaces, (fractional) Sobolev spaces, Besov s...

"Theory of Function Spaces II" deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales os spaces cover many well-known function spaces such as H?lder-Zygmund spaces, (fractional) Sobolev spaces, Besov s...

This volume of the "Mathematics Studies" series presents work done on composition operators during the last 25 years. Composition operators form a simple but interesting class of operators having interactions with different branches of mathematics and mat...

Narrow operators are those operators defined on function spaces which are "small" at signs, i.e. at {-1,0,1}-valued functions. Numerous works and research papers exist on these, but no coherent monograph yet to place them in context. This book gives compr...

Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as HĂ¶lder-Zygmund spaces, (fractional) Sobolev spaces, Besov spa...

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in anal...

This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in anal...

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variatio...