A note on the integral criterion for spectral dichotomy of regular pencils.
A Note on the Measure of Solvability
Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.
A note on the minimal essential set of coincident points for set-valued mappings.
A note on the minimax principle for -positive operators
A Note on the Paper "Hermitian Operators on C(X, E) and Banach-Stone Theorem" by R.J. Fleming and J.E.Jamison.
A note on the paper of Shütt "Unconditionality in tensor products''
A note on the parabolic differential and difference equations.
A note on the periods of periodic solutions of some autonomous functional differential equations.
A note on the powers of Cesàro bounded operators
In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator on a Hilbert space with a single spectrum satisfies
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.