On the points of multiplicity of monotone operators
On the Pointwise Ergodic Theorem in
On the pointwise ergodic theorems in (1
On the poles of the local resolvent.
On the polynomial numerical hull of a normal matrix.
On the position of the space of representable operators in the space of linear operators
We show results about the existence and the nonexistence of a projection from the space of all linear and bounded operators from into onto the subspace of all representable operators.
On the positive absolutely summing operators on the space Lp(μ,X).
On the positivity of semigroups of operators
In a Banach space , let be a -semigroup with generating operator . For a cone ...
On the positivity of the unit element in a normed lattice ordered algebra
On the potential operators associated with a semigroup
On the power boundedness of certain Volterra operator pencils
Let V be the classical Volterra operator on L²(0,1), and let z be a complex number. We prove that I-zV is power bounded if and only if Re z ≥ 0 and Im z = 0, while I-zV² is power bounded if and only if z = 0. The first result yields as n → ∞, an improvement of [Py]. We also study some other related operator pencils.
On the powers of quasihomogeneous Toeplitz operators
We present sufficient conditions for the existence of th powers of a quasihomogeneous Toeplitz operator , where is a radial polynomial function and , are natural numbers. A large class of examples is provided to illustrate our results. To our best knowledge those examples are not covered by the current literature. The main tools in the proof of our results are the Mellin transform and some classical theorems of complex analysis.
On the principal eigenvalue of elliptic operators in and applications
Two generalizations of the notion of principal eigenvalue for elliptic operators in are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semilinear problems in the whole space. We also indicate several outstanding open problems and formulate some conjectures.
On the probabilistic domain invariance.
On the problem of convergence of a bounded-below sequence of symmetric forms for the Schrödinger operators
On the problem of invariance under holomorphic functions for a set of continuity points of the spectrum function
On the problem of retracting balls onto their boundary.
On the product of self-adjoint operators.
On the projection constants of some topological spaces and some applications.
On the Putnam--Fuglede theorem.