Generalised Limits for Vector Valued Sequences

2020 ◽  
pp. 198-202
Author(s):  
Ajaya Kumar Singh
Keyword(s):  
Banach Spaces ◽  
Almost Convergence ◽  
Banach Limits ◽  
Vector Valued

The object of the present paper is to introduce the extension of the concept of Banach limits for vector valued sequences and we prove the existence of Banach limits for vector valued sequences. Also introduced Banach spaces X,X^*,X^(**) 1-complemented in their bi duals admit vector valued Banach limits. Lastly we propose Lorentz’s vector valued intrinsic characterisation of almost convergence.

scholarly journals Extremal properties of the set of vector-valued Banach limits

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Francisco Javier García-Pacheco
Keyword(s):  
Banach Spaces ◽  
Banach Limits ◽  
Vector Valued ◽  
Extremal Properties

AbstractIn this manuscript we find another class of real Banach spaces which admit vector-valued Banach limits different from the classes found in [6, 7]. We also characterize the separating subsets of ℓ

scholarly journals Constructing Banach spaces of vector-valued sequences with special properties

2015 ◽  
Vol 64 (3) ◽  
pp. 539-554 ◽  
Author(s):  
Geraldo Botelho ◽  
Vinícius Fávaro
Keyword(s):  
Banach Spaces ◽  
Vector Valued

scholarly journals Multipliers on Vector Valued Bergman Spaces

2002 ◽  
Vol 54 (6) ◽  
pp. 1165-1186 ◽  
Author(s):  
Oscar Blasco ◽  
José Luis Arregui
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Bergman Space ◽  
Unit Disc ◽  
Bergman Spaces ◽  
Complex Banach Space ◽  
Bounded Operators ◽  
Taylor Coefficients ◽  
Vector Valued

AbstractLet X be a complex Banach space and let Bp(X) denote the vector-valued Bergman space on the unit disc for 1 ≤ p < ∞. A sequence (Tn)n of bounded operators between two Banach spaces X and Y defines a multiplier between Bp(X) and Bq(Y) (resp. Bp(X) and lq(Y)) if for any function we have that belongs to Bq(Y) (resp. (Tn(xn))n ∈ lq(Y)). Several results on these multipliers are obtained, some of them depending upon the Fourier or Rademacher type of the spaces X and Y. New properties defined by the vector-valued version of certain inequalities for Taylor coefficients of functions in Bp(X) are introduced.

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