Extreme points in duals of operator spaces

Ruess, Wolfgang M.; Stegall, Charles

doi:10.1007/bf01457455

Cited by 73 publications

(37 citation statements)

References 21 publications

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“…Consequently, J * preserves extreme points. But extB 1 (X ∧ ⊗ Y * ) are just the atoms of norm 1 [22]. Hence, J * (x ⊗ y * ) is either an atom or an Step…”

Section: Isometries Of L(x Y)mentioning

confidence: 99%

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Isometries of certain operator spaces

Alwardi

2003

Proc. Amer. Math. Soc.

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Abstract. Let X and Y be Banach spaces, and L(X, Y ) be the spaces of bounded linear operators from X into Y. In this paper we give full characterization of isometric onto operators of L(X, Y ), for a certain class of Banach spaces, that includes p , 1 < p < ∞. We also characterize the isometric onto operators of L(c 0 ) and K( 1 ), the compact operators on 1 . Furthermore, the multiplicative isometric onto operators of L( 1 ), when multiplication on L( 1 ) is taken to be the Schur product, are characterized. IntroductionLet X and Y be Banach spaces, and L(X, Y ) the space of bounded linear oper- [12], it was proved that every isometry of a semisimple commutative Banach algebra that preserves the identity is multiplicative. In this paper, we give a full characterization of isometric onto operators of L(X, Y ), for a class of Banach spaces that includes p , 1 < p < ∞. Isometric onto operators of L(c 0 ), and K( 1 ), the compact operators on 1 , are also fully characterized in this paper. Furthermore, multiplicative isometric onto operators of L( 1 ) when multiplication on L( 1 ) is taken to be the Schur product are characterized.Throughout this paper, if X is a Banach space, X * is the dual ofwhere the sum is a direct summand, in the sense, if

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“…Consequently, J * preserves extreme points. But extB 1 (X ∧ ⊗ Y * ) are just the atoms of norm 1 [22]. Hence, J * (x ⊗ y * ) is either an atom or an Step…”

Section: Isometries Of L(x Y)mentioning

confidence: 99%

“…Since J is an isometry, J preserves extreme points, and consequently J preserves atoms, noting that extreme points of X ∧ ⊗ Y * are atoms of norm one [22]. Set…”

Section: Consequently J(t ) Is Compactmentioning

confidence: 99%

Isometries of certain operator spaces

Alwardi

2003

Proc. Amer. Math. Soc.

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“…. , r. By (12), there follows that 0 ∈ P Vr (B) and dim span{x j l ⊗ e j l |V r } < r, where dimV r = r. It means that there exists V ∈ V r \ {0} such that…”

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confidence: 99%

Best approximation in Chebyshev subspaces of L(l1n,l1n)

Kowynia¹

2009

OpMath

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“…But every extreme point of E(T) is an extreme point V of 5i((X ® F)*). Thus, by the result of Ruess and Stegall, [10], the extreme points of E(T) are of the form A -x* <8> y*, where a;* and y* are extreme points of Si(X*) and S^Y*), respectively. Thus, if x* ® y* G Ext(E(T)), then (x* ® y*)(T) = (Tx*,y*) = ||2V|| = 1.…”

Section: Is a Smooth Point; (Ii) T (As An Operator: X* -• Y) Attains mentioning

confidence: 89%

Smooth Points of Unit Balls of Operator and Function Spaces

Khalil

1996

Demonstratio Mathematica

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Extreme points in duals of operator spaces

Cited by 73 publications

References 21 publications

Isometries of certain operator spaces

Isometries of certain operator spaces

Best approximation in Chebyshev subspaces of L(l1n,l1n)

Smooth Points of Unit Balls of Operator and Function Spaces

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