Normed Algebras



Normed Algebras
Publisher: Wolters-Noordhoff | pages: 612 | 1972 | ISBN: 9001614752 | DJVU | 5,8 mb

The theory of normed algebras, although of recent origin, has developed into an extensive branch off functional analysis; it now has numerous applications in various other branches of mathematics. The first cycle of papers devoted to concrete normed algebras, i.e. algebras of bounded linear operators in Hilbert space, was begun in 1930 by YON NEUMANN and then continued in the works of MURAY and YON NEUMANN. The advantage of considering algebras of operators was already apparent in these works. However, it was the abstract point of view which turned out to be most fruitful; from this viewpoint, the nature of the elements of the algebra does not play any role, so that a normed algebra is simply an arbitrary set of elements which forms an algebra in the algebraic sense and which is, furthermore, provided with a norm which satisfies simple requirements.


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