Computing subdifferential limits of operators on Banach spaces

• Autorzy: Rao T. S. S. R. K.

Identyfikatory

DOI

10.1515/jaa-2022-1036

• Języki publikacji: EN

Abstrakty

EN

Let X, Y be real, infinite-dimensional Banach spaces. Let L(X, Y) be the space of bounded operators. An important aspect of understanding differentiability of the operator norm at A ∈ L(X, Y) is to estimate the limit (which always exists) lim_t→0+ ‖A + tB‖ − ‖A‖ / t for B ∈ L(X, Y), using the values of B on the state space S_A = {τ ∈ L(X, Y)∗ : τ(A) = ‖A‖, ‖τ‖ = 1}. In this paper, we give several examples of Banach spaces, including the ℓ^p spaces (for 1 < p < ∞) where a more tangible estimate is possible, under additional hypotheses on A. We also use the notion of norm-weak upper-semi-continuity (usc, for short) of the preduality map to achieve this. Our results also show that the operator subdifferential limit is related to the corresponding subdifferential limit of the vectors in the range space, when A∗∗ attains its norm.

Słowa kluczowe

EN

subdifferential of the norm; preduality map; smooth points; spaces of operators; tensor product spaces

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2023
• Tom: Vol. 29, nr 2
• Strony: 297--302
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Rao T. S. S. R. K.

• Department of Mathematics, Shiv Nadar University, Delhi (NCR), India

• https://orcid.org/0000-0003-0599-9426

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).