On some classical properties of normed spaces via generalized vector valued almost convergence
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Mahmut Karakuş
Abstract
Recently, the authors interested some new problems on multiplier spaces of Lorentz’ almost convergence and fλ-convergence as a generalization of almost convergence. fλ-convergence is firstly introduced by Karakuş and Başar, and used for some new characterizations of completeness and barrelledness of the spaces through weakly unconditionally Cauchy series in a normed space X and its continuous dual X*. In the present paper, we deal with fλ-convergence to have some inclusion relations between the vector valued spaces obtained from this type convergence and corresponding classical sequence spaces, and to give new characterizations of some classical properties like completeness, reflexivity, Schur property and Grothendieck property of normed spaces. By the way, we give a characterization of finite-dimensional normed spaces.
( Communicated by Gregor Dolinar )
Acknowledgement
The authors have also benefited much from the constructive report of the anonymous referee. So, they are thankful for his/her valuable comments on the first draft of this paper which improved the presentation and readability.
References
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© 2022 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces
Articles in the same Issue
- Prof. RNDr. Július korbaš, CSC. passed away
- Kalmbach measurability In d0-algebras
- Quantifiers on L-algebras
- Ideals of functions with compact support in the integer-valued case
- An algebraic study of the logic S5’(BL)
- Triangular numbers and generalized fibonacci polynomial
- A general matrix series inversion pair and associated polynomials
- Quantum ostrowski type inequalities for pre-invex functions
- Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function
- Approximating families for lattice outer measures on unsharp quantum logics
- On a generalized Lamé-Navier system in ℝ3
- Coercive and noncoercive elliptic problems with variable exponent Laplacian under Robin boundary conditions
- On some classical properties of normed spaces via generalized vector valued almost convergence
- Fan-Hemicontinuity for the gradient of the norm in Hilbert space
- Solvability of mixed problems for heat equations with two nonlocal conditions
- The global harnack estimates for a nonlinear heat equation with potential under finsler-geometric flow
- A note on set-star-K-Menger spaces
- A bivariate extension of the Omega distribution for two-dimensional proportional data
- Bernstein polynomials based iterative method for solving fractional integral equations
- The symmetric 4-Player gambler’s problem with unequal initial stakes
- Enveloping action: Convergence spaces
