Smooth points of certain operator spaces

Kittaneh, Fuad; Younis, Rahman

doi:10.1007/bf01198920

Cited by 20 publications

(13 citation statements)

References 5 publications

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“…Similar to the first part of (e) => (f) one can derive Theorem 2 of [5] from the equivalence of (1) and (2). It seems to be much easier to check if (2) holds than the condition on the essential norm of T in [5].…”

Section: C) => (D) Is Obvious (D) => (E)mentioning

confidence: 94%

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Differentiability of the Norm in Von Neumann Algebras

Taylor¹,

Werner²

1993

Proceedings of the American Mathematical Society

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Section: C) => (D) Is Obvious (D) => (E)mentioning

confidence: 94%

“…Recently, Kittaneh and Younis [5] characterized the smooth points in 93 (^), the Banach algebra of all bounded linear operators on a Hilbert space %?. On the other hand, the smooth points in F°°(ft, Z, p), for a measure space (ft, I, p) , have been known for a long time.…”

Section: Introductionmentioning

confidence: 99%

Differentiability of the Norm in Von Neumann Algebras

Taylor¹,

Werner²

1993

Proceedings of the American Mathematical Society

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“…It is well known (see [7] and the references therein) that, for 1 < p < ∞, C p is a uniformly convex Banach space. Therefore, every nonzero T ∈ C p is a smooth point and, in this case, the support functional of T is given by…”

Section: Preliminaries Let T ∈ B(h) Be Compact and Let S 1 (X) ≥ S 2mentioning

confidence: 99%

Some versions of Anderson′s and Maher′s inequalities II

Mecheri

2003

International Journal of Mathematics and Mathematical Sciences

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“…As an application of these results on Birkhoff-James orthogonality and operator norm attainment, we prove certain characterizations of smoothness of operators. This is a classical area of research in the geometry of Banach spaces and has been studied in great detail by several mathematicians including Holub [7], Heinrich [5], Hennefeld [6], Abatzoglou [1], Kittaneh and Younis [9]. Smoothness of bounded linear operators on some particular spaces like ℓ p spaces, etc.…”

mentioning

confidence: 99%

Birkhoff–James orthogonality and smoothness of bounded linear operators

Paul

Sain

Ghosh

2016

Linear Algebra and its Applications

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Abstract. We present a sufficient condition for smoothness of bounded linear operators on Banach spaces for the first time. Let T, A ∈ B(X, Y), where X is a real Banach space and Y is a real normed linear space. We find sufficient condition for T ⊥ B A ⇔ T x⊥ B Ax for some x ∈ S X with T x = T , and use it to show that T is a smooth point in B(X, Y) if T attains its norm at unique (upto muliplication by scalar) vector x ∈ S X , T x is a smooth point of Y and sup y∈C T y < T for all closed subsets C of S X with d(±x, C) > 0. For operators on a Hilbert space H we show that T ⊥ B A ⇔ T x⊥ B Ax for some x ∈ S H with T x = T if and only if the norm attaining set M T = {x ∈ S H : T x = T } = S H 0 for some finite dimensional subspace H 0 and T Ho ⊥ < T . We also characterize smoothness of compact operators on normed spaces and bounded linear operators on Hilbert spaces.

show abstract

Smooth points of certain operator spaces

Cited by 20 publications

References 5 publications

Differentiability of the Norm in Von Neumann Algebras

Differentiability of the Norm in Von Neumann Algebras

Some versions of Anderson′s and Maher′s inequalities II

Birkhoff–James orthogonality and smoothness of bounded linear operators

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