Strong regularity and generalized inverses in jordan systems

López, Antonio Fernández; Rus, Eulalia García; Campos, Esperanza Sánchez; Molina, Mercedes Siles

doi:10.1080/00927879208824440

Cited by 20 publications

(4 citation statements)

References 12 publications

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“…The studies on von Neumann regular elements in Jordan triple systems began with the contributions of Loos [36] and Fernández-López, García Rus, Sánchez Campos, and Siles Molina [16]. We recall that an element a in a Jordan triple system E is called von Neumann regular if a ∈ Q(a)(E) and strongly von Neumann regular when a ∈ Q(a) 2 (E).…”

Section: Von Neumann Regularity and Brown-pedersen Invertibilitymentioning

confidence: 99%

“…Given an element a in a complex Jordan triple system E, the symbol Q(a) will denote the conjugate linear operator on E given by Q(a)(x) := {a, x, a}. It is known that the fundamental identity The studies on von Neumann regular elements in Jordan triple systems began with the contributions of Loos [36] and Fernández-López, García Rus, Sánchez Campos, and Siles Molina [16]. We recall that an element a in a Jordan triple system E is called von Neumann regular if a ∈ Q(a)(E) and strongly von Neumann regular when a ∈ Q(a) 2 (E).…”

Section: Introductionmentioning

confidence: 99%

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Approximation and Convex Decomposition by Extremals and the -Function in Jbw*-Triples

Jamjoom

Siddiqui

Tahlawi

et al. 2015

The Quarterly Journal of Mathematics

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We establish new estimates to compute the λ-function of Aron and Lohman on the unit ball of a JB * -triple. It is established that for every Brown-Pedersen quasi-invertible element a in a JB * -triple, for every Brown-Pedersen quasi-invertible element a in E1, where mq(a) is the square root of the quadratic conorm of a. For an element a in E1 which is not Brown-Pedersen quasi-invertible we can only estimate that λ(a) ≤ 1 2 (1−αq(a)). A complete description of the λ-function on the closed unit ball of every JBW * -triple is also provided, and as a consequence, we prove that every JBW * -triple satisfies the uniform λ-property.

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Section: Von Neumann Regularity and Brown-pedersen Invertibilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximation and Convex Decomposition by Extremals and the -Function in Jbw*-Triples

Jamjoom

Siddiqui

Tahlawi

et al. 2015

The Quarterly Journal of Mathematics

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“…The equivalence of (i) and (ii) is contained in [20], Lemma 4.1, which relies on results of [9]. Denote by F the smallest closed (complex) subtriple of E that contains a.…”

Section: ) the Inner Ideal Q(a)e Is Closed And Complemented In Ementioning

confidence: 99%

“…Then there is a unique locally compact subset Ω ⊂ R with Ω > 0 and Ω ∪{0} compact together with a unique triple isomorphism ϕ : F → C 0 (Ω) such that ϕ(a) = id Ω . Furthermore, a is regular if and only if Ω is compact (compare [9], [20]), and then ϕ(a † ) = 1/ϕ(a). Furthermore, the sequence of all ϕ(c −n (a)), n ≥ 1, converges locally uniformly on Ω to the function ≡ 1, which is in C 0 (Ω) if and only if Ω is compact.…”

Section: ) the Inner Ideal Q(a)e Is Closed And Complemented In Ementioning

confidence: 99%

On Grassmannians associated with JB*-triples

Kaup¹

2001

Math Z

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An illustrating exampleWe illustrate our considerations in the following special situation: Let E := C n×m be the space of all complex n × m-matrices where 1 ≤ n ≤ m are fixed integers in the following. Every matrix z is considered as an operator C m → C n between finite-dimensional Hilbert spaces and z is the corresponding operator norm, i.e.is the open unit ball of E where z * = z is the transposed conjugate of z. It is known that the ball B is homogeneous under biholomorphic automorphisms and hence is an example of a bounded symmetric domain. Consider on E the linear transformation groupThen Γ is a complex Lie group that has precisely n + 1 orbits E 0 , . . . , E n in E -each E r is the (locally closed) complex submanifold of all matrices of rank r. Clearly, E r−1 is in the closure of E r for every 1 ≤ r ≤ n and E n is the unique open orbit. For every pair of integers p, q ≥ 0 let G p,q be the Grassmannian of all p-planes in C p+q . Then G p,q is a compact symmetric hermitian manifold of dimension pq holomorphically equivalent to G q,p . Every E r is in a canonical way a Γ -equivariant holomorphic fibre bundle Supported by a grant from the German-Israeli Foundation (GIF), I-0415-023.06/95.

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Hermitian Jordan Triple Systems and the Automorphisms of Bounded Symmetric Domains

Kaup

1994

Non-Associative Algebra and Its Applications

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Strong regularity and generalized inverses in jordan systems

Cited by 20 publications

References 12 publications

Approximation and Convex Decomposition by Extremals and the -Function in Jbw*-Triples

Approximation and Convex Decomposition by Extremals and the -Function in Jbw*-Triples

On Grassmannians associated with JB*-triples

Hermitian Jordan Triple Systems and the Automorphisms of Bounded Symmetric Domains

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