Polar decomposition approach to Reid's inequality.
Polar decomposition under perturbations of the scalar product.
Polar lattices from the point of view of nuclear spaces.
The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.
Polinomios ortogonales asociados con problemas espectrales
Polynomial approximations and universality
We give another version of the recently developed abstract theory of universal series to exhibit a necessary and sufficient condition of polynomial approximation type for the existence of universal elements. This certainly covers the case of simultaneous approximation with a sequence of continuous linear mappings. In the case of a sequence of unbounded operators the same condition ensures existence and density of universal elements. Several known results, stronger statements or new results can be...
Polynomially compact derivations on Banach algebras
We consider a continuous derivation D on a Banach algebra 𝓐 such that p(D) is a compact operator for some polynomial p. It is shown that either 𝓐 has a nonzero finite-dimensional ideal not contained in the radical rad(𝓐) of 𝓐 or there exists another polynomial p̃ such that p̃(D) maps 𝓐 into rad(𝓐). A special case where Dⁿ is compact is discussed in greater detail.
Polynomially compact elements of Banach algebras
Positive Approximate Identities and Lattice-Ordered Dual spaces.
Positive Compact Operators on Banach Lattices.
Positive definite diagonal sequences
Positive L¹ operators associated with nonsingular mappings and an example of E. Hille
E. Hille [Hi1] gave an example of an operator in L¹[0,1] satisfying the mean ergodic theorem (MET) and such that supₙ||Tⁿ|| = ∞ (actually, ). This was the first example of a non-power bounded mean ergodic L¹ operator. In this note, the possible rates of growth (in n) of the norms of Tⁿ for such operators are studied. We show that, for every γ > 0, there are positive L¹ operators T satisfying the MET with lim supn→ ∞ ||Tⁿ||/n1-γ₀ = 0A class of numerical sequences αₙ, intimately related to the...
Positive linear maps of matrix algebras
A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.
Positive Matrix Functions on the Bitorus with Prescribed Fourier Coefficients in a Band.
Positive operator bimeasures and a noncommutative generalization
For C*-algebras A and B and a Hilbert space H, a class of bilinear maps Φ: A× B → L(H), analogous to completely positive linear maps, is studied. A Stinespring type representation theorem is proved, and in case A and B are commutative, the class is shown to coincide with that of positive bilinear maps. As an application, the extendibility of a positive operator bimeasure to a positive operator measure is shown to be equivalent to various conditions involving positive scalar bimeasures, pairs of...
Positive operators and approximation in function spaces on completely regular spaces.
Positive Schatten class Toeplitz operators on the ball
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
Positive Schatten-Herz class Toeplitz operators on the ball.
Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
Positive Selfadjoint Extensions of Positive Symmetric Subspace.
Positive Toeplitz operators between the pluriharmonic Bergman spaces
We study Toeplitz operators between the pluriharmonic Bergman spaces for positive symbols on the ball. We give characterizations of bounded and compact Toeplitz operators taking a pluriharmonic Bergman space into another for in terms of certain Carleson and vanishing Carleson measures.