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Renewed interest in vector spaces and linear algebras has spurred
the search for large algebraic structures composed of mathematical
objects with special properties. Bringing together research that
was otherwise scattered throughout the literature, Lineability: The
Search for Linearity in Mathematics collects the main results on
the conditions for the existence of large algebraic substructures.
It investigates lineability issues in a variety of areas, including
real and complex analysis. After presenting basic concepts about
the existence of linear structures, the book discusses lineability
properties of families of functions defined on a subset of the real
line as well as the lineability of special families of holomorphic
(or analytic) functions defined on some domain of the complex
plane. It next focuses on spaces of sequences and spaces of
integrable functions before covering the phenomenon of universality
from an algebraic point of view. The authors then describe the
linear structure of the set of zeros of a polynomial defined on a
real or complex Banach space and explore specialized topics, such
as the lineability of various families of vectors. The book
concludes with an account of general techniques for discovering
lineability in its diverse degrees.
Renewed interest in vector spaces and linear algebras has spurred
the search for large algebraic structures composed of mathematical
objects with special properties. Bringing together research that
was otherwise scattered throughout the literature, Lineability: The
Search for Linearity in Mathematics collects the main results on
the conditions for the existence of large algebraic substructures.
It investigates lineability issues in a variety of areas, including
real and complex analysis. After presenting basic concepts about
the existence of linear structures, the book discusses lineability
properties of families of functions defined on a subset of the real
line as well as the lineability of special families of holomorphic
(or analytic) functions defined on some domain of the complex
plane. It next focuses on spaces of sequences and spaces of
integrable functions before covering the phenomenon of universality
from an algebraic point of view. The authors then describe the
linear structure of the set of zeros of a polynomial defined on a
real or complex Banach space and explore specialized topics, such
as the lineability of various families of vectors. The book
concludes with an account of general techniques for discovering
lineability in its diverse degrees.
The fundamental contributions made by the late Victor Lomonosov in
several areas of analysis are revisited in this book, in
particular, by presenting new results and future directions from
world-recognized specialists in the field. The invariant subspace
problem, Burnside's theorem, and the Bishop-Phelps theorem are
discussed in detail. This volume is an essential reference to both
researchers and graduate students in mathematical analysis.
Inequalities play a central role in mathematics with various
applications in other disciplines. The main goal of this
contributed volume is to present several important matrix,
operator, and norm inequalities in a systematic and self-contained
fashion. Some powerful methods are used to provide significant
mathematical inequalities in functional analysis, operator theory
and numerous fields in recent decades. Some chapters are devoted to
giving a series of new characterizations of operator monotone
functions and some others explore inequalities connected to
log-majorization, relative operator entropy, and the Ando-Hiai
inequality. Several chapters are focused on Birkhoff-James
orthogonality and approximate orthogonality in Banach spaces and
operator algebras such as C*-algebras from historical perspectives
to current development. A comprehensive account of the boundedness,
compactness, and restrictions of Toeplitz operators can be found in
the book. Furthermore, an overview of the Bishop-Phelps-Bollobas
theorem is provided. The state-of-the-art of Hardy-Littlewood
inequalities in sequence spaces is given. The chapters are written
in a reader-friendly style and can be read independently. Each
chapter contains a rich bibliography. This book is intended for use
by both researchers and graduate students of mathematics, physics,
and engineering.
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