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Search Results: 1 - 10 of 4781 matches for " Direct sum of Banach spaces "
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Strict convexity of absolute norms on and direct sums of banach spaces
Takahashi Yasuji,Kato Mikio,Saito Kichi-Suke
Journal of Inequalities and Applications , 2002,
Abstract: We show that an absolute normalized norm on is strictly convex if and only if the corresponding convex function on is strictly convex. In this context the monotonicity property of these norms is discussed. We also introduce the notion of the direct sum of Banach spaces and equipped with the associated norm with and characterize the strict convexity of .
Spectrum of the direct sum of operators
Elif Otkun Cevik,Zameddin I. Ismailov
Electronic Journal of Differential Equations , 2012,
Abstract: We study the connection between spectral properties of direct the sum of operators in the direct sum of Hilbert spaces and its coordinate operators.
Compact inverses of multipoint normal differential operators for first order
Zameddin I. Ismailov,Elif Otkun Cevik,Erdal Unluyol
Electronic Journal of Differential Equations , 2011,
Abstract: In this work, we describe all normal extensions of a multipoint minimal operators generated by linear multipoint differential-operator expressions for first order in the Hilbert space of vector functions, in terms of boundary values at the endpoints of infinitely many separated subintervals. Also we investigate compactness properties of the inverses of such extensions.
Direct and inverse problems for systems of singular differential boundary-value problems
Angelo Favini,Alfredo Lorenzi,Hiroki Tanabe
Electronic Journal of Differential Equations , 2012,
Abstract: Real interpolation spaces are used for solving some direct and inverse linear evolution problems in Banach spaces, on the ground of space regularity assumptions.
Von Neumann–Jordan constant for Lebesgue–Bochner spaces
Kato Mikio,Takahashi Yasuji
Journal of Inequalities and Applications , 1998,
Abstract: The von Neumann–Jordan (NJ-) constant for Lebesgue–Bochner spaces is determined under some conditions on a Banach space . In particular the NJ-constant for as well as (the space of -Schatten class operators) is determined. For a general Banach space we estimate the NJ-constant of , which may be regarded as a sharpened result of a previous one concerning the uniform non-squareness for . Similar estimates are given for Banach sequence spaces ( -sum of Banach spaces ), which gives a condition by NJ-constants of 's under which is uniformly non-square. A bi-product concerning 'Clarkson's inequality' for and is also given.
Multipoint normal differential operators of first order
Zameddin I. Ismailov
Opuscula Mathematica , 2009,
Abstract: In this paper we discuss all normal extensions of a minimal operator generated by a linear multipoint differential-operator expression of first order in the Hilbert space of vector-functions on the finite interval in terms of boundary and interior point values. Later on, we investigate the structure of the spectrum, its discreteness and the asymptotic behavior of the eigenvalues at infinity for these extensions.
Certain Banach spaces in connection with best approximation
Antonio Martinón,F. Pérez-Acosta
Le Matematiche , 1998,
Abstract: See directly the article.
The Index of Invariant Subspaces of Bounded below Operators on Banach Spaces  [PDF]
George Chailos
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.22018
Abstract: For an operator on a Banach space , let be the collection of all its invariant subspaces. We consider the index function on and we show, amongst others, that if is a bounded below operator and if , , then If in addition are index 1 invariant subspaces of , with nonzero intersection, we show that . Furthermore, using the index function, we provide an example where for some , holds .
A Study of Periodic Solution of a Duffing’s Equation Using Implicit Function Theorem  [PDF]
E. O. Eze, J. N. Ezeora, U. E. Obasi
Open Journal of Applied Sciences (OJAppS) , 2018, DOI: 10.4236/ojapps.2018.810036
Abstract: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the origin, a unique periodic solution was obtained.
The strong WCD property for Banach spaces
Dave Wilkins
International Journal of Mathematics and Mathematical Sciences , 1995, DOI: 10.1155/s0161171295000081
Abstract: In this paper, we introduce weakly compact version of the weakly countably determined (WCD) property, the strong WCD (SWCD) property. A Banach space X is said to be SWCD if there s a sequence (An) of weak ¢ — compact subsets of X ¢ — ¢ — such that if K ¢ X is weakly compact, there is an (nm) ¢ N such that K ¢ ¢ m=1 ¢ Anm ¢ X. In this case, (An) is called a strongly determining sequence for X. We show that SWCG ¢ ’SWCD and that the converse does not hold in general. In fact, X is a separable SWCD space if and only if (X, weak) is an ¢ μ0-space. Using c0 for an example, we show how weakly compact structure theorems may be used to construct strongly determining sequences.
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