Results 201 to 210 of about 2,451 (228)
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Banach-Saks exponent of certain Banach spaces of sequences
Mathematical Notes of the Academy of Sciences of the USSR, 1982Translation from Mat. Zametki 32, No.5, 613-625 (Russian) (1982; Zbl 0505.46005).
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On the boundedness of one recurrent sequence in a banach space
Ukrainian Mathematical Journal, 2009Summary: We establish necessary and sufficient conditions under which a sequence \(x_0=y_0\), \(x_{n+1}=Ax_n+y_{ n+1}\), \(n\geq0\), is bounded for each bounded sequence \(\{y_n:n\geq0\}\subset\{x\in\bigcup_{n=1}^{\infty}D(A^n)|\sup_{n\geq0}\mid A^nx\|
Gorodnij, M. F., Vyatchaninov, O. V.
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COEFFICIENT SEQUENCES IN HILBERT AND BANACH SPACE EXPANSIONS
Mathematics of the USSR-Izvestiya, 1971In 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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Representation of the space spanned by a sequence in a Banach space
Archiv der Mathematik, 1984A sequence \((x_ n)\) of a Banach space B is said to be pseudo basic with brackets if there exists an increasing sequence \((q_ n)\) of positive integers so that, setting \(q_ 0=0\), \(x=\sum^{\infty}_{m=0}(\sum^{q_{m+1}}_{n=q_ m+1}a_ nx_ n)\) for every x of \(\overline{span}(x_ n)\), where \((a_ n)\) depends on x while \((q_ n)\) does not depend on x;
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On Operators Acting on Convergent Sequences in Banach Spaces
Mathematische Nachrichten, 1996AbstractOur concern is to find a representation theorem for operators in B(c(X), c(Y)) where X and Y are Banach spaces with Y containing an isomorphic copy of c0. Cass and Gao [1] obtained a representation theorem that always applies if Y does not contain an isomorphic copy of c0.
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Relative Position, Sequences and Operators in Banach Spaces
Mathematische Nachrichten, 1994This 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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On Relationships Amongst Certain Spaces Of Sequences In An Arbitrary Banach Space
Canadian Journal of Mathematics, 19561. Introduction. Let X be a Banach space (B-space). A sequence {s(i)} in X is unconditionally summable if and only if every rearrangement of the series Σis(i) is convergent. The set of unconditionally summable sequences in X will be written as U(X). In this paper several classes of summable sequences in X will be compared with one another.
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On the geometry of sequences in Banach spaces
Archiv der Mathematik, 1983Plans, Antonio, Reyes, Andres
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