A remark on the best approximation in the mean of vector-valued functions

Smirnov, Georgey S.

doi:10.1007/bf01060574

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2023

2024

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“…Further, when X is a complex Banach space we have a slightly weaker charaterization, but for a large class of spaces, namely smooth Banach spaces. We would deploy few techniques of Smirnov [13] to prove the necessary part of the following result. Theorem 3.1.…”

Section: Best Approximation Inmentioning

confidence: 99%

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Birkhoff-James orthogonality in certain tensor products of Banach spaces

Mohit¹,

Jain²

2023

Operators and Matrices

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In this article, the relationship between Birkhoff-James orthogonality of elementary tensors in certain tensor product spaces with the Birkhoff-James orthogonality of individual elements in their respective spaces is studied. Mathematics subject classification (2020): 46J10, 46A32, 46M05, 46L06. Keywords and phrases: Birkhoff-James orthogonality, cross norm, injective tensor product, minimal tensor product of C * -algebras, strong Birkhoff-James orthogonality.

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Section: Best Approximation Inmentioning

confidence: 99%

“…A natural question arises that what can be said about the approximation for the vector valued integrable functions. In 1989, Smirnov [13] characterized the elements of P G (f ) for f ∈ C([0, 1], X) \ U, for a real smooth Banach space X and a convex subset U of C([0, 1], X)(equipped with the integral-norm).…”

Section: Introductionmentioning

confidence: 99%