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Some multiplicative preservers on B(H)

✍ Scribed by Lajos Molnár

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
101 KB
Volume
301
Category
Article
ISSN
0024-3795

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✦ Synopsis

In this paper we describe the form of those continuous multiplicative maps on B(H ) (H being a separable complex Hilbert space of dimension not less than 3) which preserve the rank, or the corank. Furthermore, we characterize those continuous * -semigroup endomorphisms of B(H ) which are spectrum non-increasing.

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✍ Gennady Bachman 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 305 KB

The study of the distribution of general multiplicative functions on arithmetic progressions is, largely, an open problem. We consider the simplest instance of this problem and establish an essentially the best possible result of the form where f is a nonnegative multiplicative function and (a, q)=