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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Introduction to the Theory of Bases (Paperback, Softcover reprint of the original 1st ed. 1969)
Loot Price: R1,431
Discovery Miles 14 310
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Introduction to the Theory of Bases (Paperback, Softcover reprint of the original 1st ed. 1969)
Series: Springer Tracts in Natural Philosophy, 18
Expected to ship within 10 - 15 working days
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Total price: R1,451
Discovery Miles: 14 510
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Since the publication of Banach's treatise on the theory of linear
operators, the literature on the theory of bases in topological
vector spaces has grown enormously. Much of this literature has for
its origin a question raised in Banach's book, the question whether
every sepa rable Banach space possesses a basis or not. The notion
of a basis employed here is a generalization of that of a Hamel
basis for a finite dimensional vector space. For a vector space X
of infinite dimension, the concept of a basis is closely related to
the convergence of the series which uniquely correspond to each
point of X. Thus there are different types of bases for X,
according to the topology imposed on X and the chosen type of
convergence for the series. Although almost four decades have
elapsed since Banach's query, the conjectured existence of a basis
for every separable Banach space is not yet proved. On the other
hand, no counter examples have been found to show the existence of
a special Banach space having no basis. However, as a result of the
apparent overconfidence of a group of mathematicians, who it is
assumed tried to solve the problem, we have many elegant works
which show the tight connection between the theory of bases and
structure of linear spaces."
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