A Note on the Product of Random Elements of a Semigroup.
A note on the range of generalized derivation.
Let L(H) denote the algebra of bounded linear operators on a complex separable and infinite dimensional Hilbert space H. For A, B ∈ L(H), the generalized derivation δA,B associated with (A, B), is defined by δA,B(X) = AX - XB for X ∈ L(H). In this note we give some sufficient conditions for A and B under which the intersection between the closure of the range of δA,B respect to the given topology and the kernel of δA*,B* vanishes.
A note on the range of the operator defined on .
A note on the regularity of the solutions to two variational inequalities involving a pseudodifferential operator.
A note on the Rellich formula in Lipschitz domains.
Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain Ω of RN and having Lipschitz coefficients in Ω. It is shown that the Rellich formula with respect to Ω and L extends to all functions in the domain D = {u ∈ H01(Ω); L(u) ∈ L2(Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.
A note on the second order boundary value problem on a half-line.
A note on the spectral mapping theorem
A note on the spectral operators of scalar type and semigroups of bounded linear operators.
A note on the stability of linear combinations of algebraic operators.
A note on the super-additive and sub-additive transformations of aggregation functions: The multi-dimensional case
For an aggregation function we know that it is bounded by and which are its super-additive and sub-additive transformations, respectively. Also, it is known that if is directionally convex, then and is linear; similarly, if is directionally concave, then and is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively.
A note on the unique solvability of a class of nonlinear equations.
A Note on Time Dependent Scattering Theory for P2 - P2 + (1 + |Q|) - 1 ... and P1 P2 + (1 + |Q|) - 1 - ... on L2 (R2).
A note on Toeplitz operators on Bergman spaces
A note on uniform boundedness principle for nonlinear operators
A note on uniformly dominated sets of summing operators.
A note on variational-type inequalities for (η,θ,δ)-pseudomonotone-type set-valued mappings in nonreflexive Banach spaces
In this paper the existence of solutions to variational-type inequalities problems for (η,θ,δ)- pseudomonotone-type set-valued mappings in nonreflexive Banach spaces introduced in [4] is considered. Presented theorem does not require a compact set-valued mapping, but requires a weaker condition 'locally bounded' for the mapping.
A note on weak estimates for oscillating kernels
A note on well-posed null and fixed point problems.
A note on γ-radonifying and summing operators
In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted -spaces.
A notion of analytic generator for groups of unbounded operators
We introduce a notion of analytic generator for groups of unbounded operators, on Banach modules, arising from Esterle’s quasimultiplier theory. Characterizations of analytic generators are given in terms of the existence of certain functional calculi. This extends recent results about C₀ groups of bounded operators. The theory is applicable to sectorial operators, representations of , and integrated groups.