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L y L*-convergencias en G(H).

M.ª Carmen de las Obras Loscertales y Nasarre (1981)

Revista Matemática Hispanoamericana

Given a real separable Hilbert space H, we denote with G(H) the geometry of closed linear subspaces of H.The strong convergence of sequences of subspaces is shown to be a L*-convergence and the weak convergence a L-convergence.The smallest L*-convergence containing the weak convergence is found, and the orthogonal image of the strong convergence, which is also a L*-convergence, is defined.

Linear maps preserving A -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there exists an...

Lipschitz extensions of convex-valued maps

Alberto Bressan, Agostino Cortesi (1986)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra che ogni funzione multivoca lipschitziana con costante di Lipschitz M , definita su un sottoinsieme di uno spazio di Hilbert H a valori compatti e convessi in n , può essere estesa su tutto H ad una funzione multivoca lipschitziana con costante minore di 7 nM. In generale, non esistono invece estensioni aventi la stessa costante di Lipschitz M .

Locally constant functions

Joan Hart, Kenneth Kunen (1996)

Fundamenta Mathematicae

Let X be a compact Hausdorff space and M a metric space. E 0 ( X , M ) is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which E 0 ( X , M ) is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of E 0 ( X , M ) as a normed linear space. We also build three first countable Eberlein...

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