Chapter X Semi-Groups in the Strong Topology

Book Id: WPLBN0000673349
Format Type: PDF eBook:
File Size: 3.16 MB
Reproduction Date: 2005

Title:	Chapter X Semi-Groups in the Strong Topology
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Chapter X Semi-Groups in the Strong Topology. (n.d.). Chapter X Semi-Groups in the Strong Topology. Retrieved from http://self.gutenberg.org/

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Mathematics document containing theorems and formulas.

Excerpt
Excerpt: In the present chapter we deal with the strong case analogues of Problems A and B of the preceding chapter. The first problem is that of a one-parameter semi-group t5 = [T(t); E > 01 of linear bounded transformations on a complex (B)-space% to itself with the property that T(h + t2)x = T(&)[T(tz)xl for all h , 52 > 0 and all x E X. We assume throughout the remainder of this treatise that T(5) is strongly continuous for t > 0. Actually this assumption is not as restrictive as it appears at first sight since strong measurability alone...