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Hyperbolic sets, shadowing and persistence for noninvertible mappings in Banach spaces

, 2022
Introduction Hyperbolic operators, projections , diagonalization Sequence spaces and substitution operators Hyperbolic sets Shadowing and persistence of hyperbolic sets Transversal homoclinic orbits Appendix Notation ...
B. Lani-Wayda
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On Subsequential Averages of Sequences in Banach Spaces

Real Analysis Exchange, 2023
This paper gives a strong contribution to the solution to the conjecture described next. Conjecture 1. Let \(\mathcal{X}\) be a Banach space, and suppose that \(x=\{x_n\}_{n=0}^{\infty}\subseteq\mathcal{X}\). Then the set \[\overline{x}^c=\left\{y\in\mathcal{X}: \exists \text{ a strictly increasing sequence } \{k_n\}\text{ s.t.
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Compact operators on the Jordan totient sequence spaces

Mathematical methods in the applied sciences, 2020
The necessary and sufficient conditions for compactness of a matrix operator between Banach spaces is obtained by utilizing the concept of the Hausdorff measure of noncompactness.
M. İlkhan, E. Kara, F. Usta
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Order spectrum of the Cesàro operator in Banach lattice sequence spaces

Positivity (Dordrecht), 2019
The discrete Cesàro operator C acts continuously in various classical Banach sequence spaces within $$ {\mathbb {C}}^{{\mathbb {N}}}.$$ C N . For the coordinatewise order, many such sequence spaces X are also complex Banach lattices [eg. $$c_0, \ell ^p $$
J. Bonet, W. Ricker
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Sequences in Banach spaces

1983
The subject of the Note is the set of all the subsequences of a linearly independent sequence of a Banach space. There are described the elementary types of this set, that is some types of subsequences such that all the other subsequences are union of these elementary types.
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Banach-Saks exponent of certain Banach spaces of sequences

Mathematical Notes of the Academy of Sciences of the USSR, 1982
Translation from Mat. Zametki 32, No.5, 613-625 (Russian) (1982; Zbl 0505.46005).
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COEFFICIENT SEQUENCES IN HILBERT AND BANACH SPACE EXPANSIONS

Mathematics of the USSR-Izvestiya, 1971
In this article we prove some theorems about the sequences of coefficients which occur for expansions relative to a basis in a Banach space, and for a certain type of basis in investigated by K. I. Babenko, namely , . As an application of our results, we prove that there exists no universal basis in a separable Hilbert space.
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Relative Position, Sequences and Operators in Banach Spaces

Mathematische Nachrichten, 1994
This note is a contribution in the research about the relative position of closed subspaces of a Banach space \(B\). In connection with the previous problem, we have among others the following questions: 1) For an \(M\)-basic sequence \((a_i)_{i\in\mathbb{N}}\) of \(B\) the knowledge of the relative position of any two subspaces \([(a_i)_{i\in S ...
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