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A general look at local principles with special emphasis on the norm computation aspect (1988)

Böttcher, A. ; Krupnik, N. ; Silbermann, B.

Springer

Integral equations and operator theory 11 (1988), S. 455-479

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ISSN: 1420-8989

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Local principles associate with every element of a Banach algebra a family of local objects in terms of which the properties of the original element can be studied. In this paper some general relations between three such principles, usually affiliated with the names of Simonenko, Allan/Douglas, and Gohberg/Krupnik, are discussed. Special attention is paid to the question on how the norm of an element can be expressed in terms of the norms of the local objects associated with it. The general theory is illustrated by some concrete results on singular integral operators and Toeplitz operators.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01199302

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