A Relation between Diagonal and Unconditional Basis Constants.
A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courant's nodal line theorem and the substantial dimension of tight polyhedral surfaces.
A relation to Hilbert's integral inequality and some base Hilbert-type inequalities.
A remark concerning Putinar's model of hyponormal weighted shifts
The question whether a hyponormal weighted shift with trace class self-commutator is the compression modulo the Hilbert-Schmidt class of a normal operator, remains open. It is natural to ask whether Putinar's construction through which he proved that hyponormal operators are subscalar operators provides the answer to the above question. We show that the normal extension provided by Putinar's theory does not lead to the extension that would provide a positive answer to the question.
A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.
The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.
A Remark on a Class of Linear Monotone Operators.
A remark on Berezanskiĭ version on spectral theorem
A remark on -spaces.
A remark on extrapolation of rearrangement operators on dyadic , 0 < s ≤ 1
For an injective map τ acting on the dyadic subintervals of the unit interval [0,1) we define the rearrangement operator , 0 < s < 2, to be the linear extension of the map , where denotes the -normalized Haar function supported on the dyadic interval I. We prove the following extrapolation result: If there exists at least one 0 < s₀ < 2 such that is bounded on , then for all 0 < s < 2 the operator is bounded on .
A remark on Fefferman-Stein's inequalities.
It is proved that, for some reverse doubling weight functions, the related operator which appears in the Fefferman Stein's inequality can be taken smaller than those operators for which such an inequality is known to be true.
A remark on Gwinner's existence theorem on variational inequality problem.
A remark on harmonic analysis of strongly almost-periodic groups of linear operators
A Remark on Invariant Pseudo-Differential Operators.
A remark on linear operators leaving a cone invariant in a Banach space
A remark on nonlinear cosine functions.
A Remark on Normal Derivations of Hilbert-Schmidt Type.
A remark on (p, q)-absolutely summing operators in -spaces
A remark on parabolic equations.
A Remark on Perturbations of Compact Operators.
A remark on p-integral and p-absolutely summing operators form into