This paper is in part a brief survey of backward shifts. However, we present several new results on backward and forward shifts which have not appeared so far. These results concern isomorphism invariance of backward and forward shifts, and the duality between these properties.
On the Generalized Resolvent in Banach Spaces
โ Scribed by M. Mbekhta
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 481 KB
- Volume
- 189
- Category
- Article
- ISSN
- 0022-247X
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๐ SIMILAR VOLUMES
## Abstract Let __X__ be a real Banach space, __ฯ__ : [0, +โ) โ โ be an increasing continuous function such that __ฯ__(0) = 0 and __ฯ__(__t__ + __s__) โค __ฯ__(__t__) + __ฯ__(__s__) for all __t__, __s__ โ [0, +โ). According to the infinite dimensional analog of the Osgood theorem if โซ^1^~0~ (__ฯ__(_
In this article we shall introduce and investigate a notion of generalized 5 5 5 5 5 5 Daugavet equation I q S q T s 1 q S q T for operators S and T on a uniformly convex Banach space into itself, where I denotes the identity operator. This extends the well-known Daugavet equation 5 5 5 5 IqT s1q T