In:
Fasciculi Mathematici, Walter de Gruyter GmbH, Vol. 59, No. 1 ( 2017-12-20), p. 107-123
Abstract:
Given any sequence a = (a n ) n≥1 of positive real numbers and any set E of complex sequences, we write E a for the set of all sequences y = (y n ) n≥1 such that y/a = (y n /a n ) n≥1 ∈ E. In this paper we deal with the solvability of the (SSIE) of the form ℓ ∞ ⊂ ℇ+F′ x where ℇ is a linear space of sequences and F′ is either c 0 , or ℓ ∞ and we solve the (SSIE) c 0 ⊂ ℇ + s x for ℇ ⊂ (s α ) ∆ and α ∈ c 0 . Then we study the (SSIE) c ⊂ ℇ + s (c) x and the (SSE) ℇ + s (c) x = c. Then we apply the previous results to the solvability of the (SSE) of the form (ℓ r p ) ∆ + F x = F for p ≥ 1 and F is any of the sets c 0 , c, or ℓ ∞ . These results extend some of those given in [8] and [9] .
Type of Medium:
Online Resource
ISSN:
0044-4413
DOI:
10.1515/fascmath-2017-0020
Language:
Unknown
Publisher:
Walter de Gruyter GmbH
Publication Date:
2017
detail.hit.zdb_id:
2584609-7
