scholarly journals Conditions of unicity of the best nonsymmetric $L_1$-approximant for vector-valued functions by one-dimensional subspace

2021 ◽  
Vol 19 ◽  
pp. 123
Author(s):  
M.Ye. Tkachenko ◽  
V.M. Traktynska
Keyword(s):  
Dimensional Subspace ◽  
Continuous Vector ◽  
One Dimensional ◽  
Vector Valued Functions ◽  
Vector Valued

The conditions of the unicity of the best nonsymmetric $L_1$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

scholarly journals Conditions of unicity of the best non-symmetric $L_1$-approximant for continuous vector-valued functions by one-dimensional subspace

2012 ◽  
Vol 20 ◽  
pp. 129
Author(s):  
M.Ye. Tkachenko ◽  
V.M. Traktyns'ka
Keyword(s):  
Sufficient Conditions ◽  
Dimensional Subspace ◽  
Necessary And Sufficient Conditions ◽  
Continuous Vector ◽  
One Dimensional ◽  
Necessary And Sufficient ◽  
Vector Valued Functions ◽  
Vector Valued

The necessary and sufficient conditions of the unicity of the best $(\overline{\alpha};\overline{\beta})$-approximant for the continuous vector-valued functions on the metric compact by one-dimensional subspace are obtained.

Spaces of Continuous Vector Functions as Duals

1988 ◽  
Vol 31 (1) ◽  
pp. 70-78 ◽  
Author(s):  
Michael Cambern ◽  
Peter Greim
Keyword(s):  
Hilbert Space ◽  
Weak Topology ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractA well known result due to Dixmier and Grothendieck for spaces of continuous scalar-valued functions C(X), X compact Hausdorff, is that C(X) is a Banach dual if, and only if, Xis hyperstonean. Moreover, for hyperstonean X, the predual of C(X) is strongly unique. Here we obtain a formulation of this result for spaces of continuous vector-valued functions. It is shown that if E is a Hilbert space and C(X, (E, σ *) ) denotes the space of continuous functions on X to E when E is provided with its weak * ( = weak) topology, then C(X, (E, σ *) ) is a Banach dual if, and only if, X is hyperstonean. Moreover, for hyperstonean X, the predual of C(X, (E, σ *) ) is strongly unique.

scholarly journals Multipliers of Modules of Continuous Vector-Valued Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Normed Spaces ◽  
Locally Compact ◽  
Continuous Vector ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Locally Compact Hausdorff Space ◽  
Locally Convex

In 1961, Wang showed that ifAis the commutativeC*-algebraC0(X)withXa locally compact Hausdorff space, thenM(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing thatHomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)),whereEandFarep-normed spaces which are also essential isometric leftA-modules withAbeing a certain commutativeF-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.

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