Abstract and Applied Analysis

A new characterization of $B$-bounded semigroups with application to implicit evolution equations

Luisa Arlotti

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Abstract

We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called B-bounded semigroups. We first determine all the properties possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T(t))t0 such that for all t0,fD(B) we can write Y(t)f=T(t)Bf. Furthermore, we compare our result with the previous ones and finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations.

Article information

Source
Abstr. Appl. Anal., Volume 5, Number 4 (2000), 227-244.

Dates
First available in Project Euclid: 10 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1049999353

Digital Object Identifier
doi:10.1155/S1085337500000336

Mathematical Reviews number (MathSciNet)
MR1885468

Zentralblatt MATH identifier
1002.47018

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30] 34G10

Citation

Arlotti, Luisa. A new characterization of $B$-bounded semigroups with application to implicit evolution equations. Abstr. Appl. Anal. 5 (2000), no. 4, 227--244. doi:10.1155/S1085337500000336. https://projecteuclid.org/euclid.aaa/1049999353


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