Let G denote a locally compact Hausdorff abelian group. Then a bounded linear operator T from L^2(G) into L^2(G) is a bounded multiplier operator if, under the Fourier transform on L^2(G ), for each function f in L^2(G), T(f) changes into a bounded function U times the Fourier transform of f. Then U is called the multiplier of T. An unbounded multiplier operator has a similar definition, but it...

for some fixed large N0; we shall call such weights admissible. Rubio de Francia [11] showed that for every w ∈ L(R) there is a nonnegative W ∈ L(R) such that ‖W‖2 ≤ Cλ‖w‖2, Cλ < ∞ if λ > 0, and the analogous weighted norm inequality for S t holds uniformly in t. He used methods related to factorization theory of operators and the proof gave no information on how to construct w from W . In [3] ...

Let A be a linear bounded operator from a couple X = (X0, X1) to a couple Y = (Y0, Y1) such that the restrictions of A on the spaces X0 and X1 have bounded inverses. This condition does not imply that the restriction of A on the real interpolation space (X0, X1)θ,q has a bounded inverse for all values of the parameters θ and q. In this paper under some conditions on the kernel of A we describe ...

Starting from the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and local spectrum, the local spectral space and the single-valued extension property of a family of linear bounded operators on a Banach space. Keeping the analogy with the classic case, we extend some of the known results from the case of a l...

In this paper we show that every power bounded operator weighted shift with commuting normal weights is similar to a contraction. As an application of this result, we reduce the problem whether every centered power bounded operator is similar to a contraction to the analogous question about quasi-invertible centered operators.

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

Let H be a Hilbert space, and A an inhabited, bounded, convex subset of B(H). We give a constructive proof that A is weak-operator totally bounded if and only if it is located relative to a certain family of seminorms that induces the strong-operator topology on B(H). 2000 Mathematics Subject Classification 03F60, 47S30 (primary)

Given bounded linear operators T1, T2 and T3, this paper investigates certain invariance properties of the operator product T1XT3 with respect to the choice of bounded linear operator X, where X is a generalized inverse of T2. Different types of generalized inverses are taken into account.

If a normalized Kähler-Ricci flow g(t), t ∈ [0,∞), on a compact Kähler manifold M , dimC M = n ≥ 3, with positive first Chern class satisfies g(t) ∈ 2πc1(M) and has curvature operator uniformly bounded in Ln-norm, the curvature operator will also be uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a Kähler-Ricci soliton.

On a bounded pseudoconvex domain in C with a plurisubharmonic Lipschitz defining function, we prove that the ∂̄-Neumann operator is bounded on Sobolev (1/2)-spaces. 0. Introduction LetD be a bounded pseudoconvex domain in C with the standard Hermitian metric. The ∂̄-Neumann operator N for (p, q)-forms is the inverse of the complex Laplacian = ∂̄ ∂̄∗ + ∂̄∗∂̄ , where ∂̄ is the maximal extension of the C...