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Characterisations of open multivalued linear operators

T. Álvarez (2006)

Studia Mathematica

The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.

Characterization of Bessel sequences.

M. Laura Arias, Gustavo Corach, Miriam Pacheco (2007)

Extracta Mathematicae

Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.

Characterization of Globally Lipschitz Nemytskiĭ Operators Between Spaces of Set-Valued Functions of Bounded φ-Variation in the Sense of Riesz

N. Merentes, J. L. Sánchez Hernández (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Let (X,∥·∥) and (Y,∥·∥) be two normed spaces and K be a convex cone in X. Let CC(Y) be the family of all non-empty convex compact subsets of Y. We consider the Nemytskiĭ operators, i.e. the composition operators defined by (Nu)(t) = H(t,u(t)), where H is a given set-valued function. It is shown that if the operator N maps the space R V φ ₁ ( [ a , b ] ; K ) into R W φ ₂ ( [ a , b ] ; C C ( Y ) ) (both are spaces of functions of bounded φ-variation in the sense of Riesz), and if it is globally Lipschitz, then it has to be of the form H(t,u(t)) = A(t)u(t)...

Characterization of Jordan derivations on 𝒥-subspace lattice algebras

Xiaofei Qi (2012)

Studia Mathematica

Let 𝓛 be a 𝒥-subspace lattice on a Banach space X and Alg 𝓛 the associated 𝒥-subspace lattice algebra. Assume that δ: Alg 𝓛 → Alg 𝓛 is an additive map. It is shown that δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = 0 if and only if δ(A) = τ(A) + δ(I)A for all A, where τ is an additive derivation; if X is complex with dim X ≥ 3 and if δ is linear, then δ satisfies δ(AB + BA) = δ(A)B + Aδ(B) + δ(B)A + Bδ(A) for any A,B ∈ Alg 𝓛 with AB + BA = I if...

Characterization of some interpolation spaces (I)

Alessandra Lunardi (1982)

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

Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.

Characterization of some interpolation spaces (II)

Alessandra Lunardi (1982)

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

Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.

Characterization of the convolution operators on quasianalytic classes of Beurling type that admit a continuous linear right inverse

José Bonet, Reinhold Meise (2008)

Studia Mathematica

Extending previous work by Meise and Vogt, we characterize those convolution operators, defined on the space ( ω ) ( ℝ ) of (ω)-quasianalytic functions of Beurling type of one variable, which admit a continuous linear right inverse. Also, we characterize those (ω)-ultradifferential operators which admit a continuous linear right inverse on ( ω ) [ a , b ] for each compact interval [a,b] and we show that this property is in fact weaker than the existence of a continuous linear right inverse on ( ω ) ( ℝ ) .

Characterization of the domain of an elliptic operator of infinitely many variables in L 2 ⁢ μ spaces

Giuseppe Da Prato (1997)

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

We consider an elliptic operator associated to a Dirichlet form corresponding to a differential stochastic equation of potential form. We characterize the domain of the operator as a subspace of W 2 , 2 ⁢ μ , where m ⁢ u is the invariant measure of the differential stochastic equation.

Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

Solving a problem of L. Schwartz, those constant coefficient partial differential operators P ( D ) are characterized that admit a continuous linear right inverse on ℰ ( Ω ) or 𝒟 ' ( Ω ) , Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P ( D ) being very hyperbolic. For Ω = R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P .

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