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...

In this paper two-dimensional Vilenkin-like systems will be investigated. We prove the Sunouchi operator is bounded from H to L for (2/3 < q ≤ 1). As a consequence, we prove the Sunouchi operator is L bounded for 1 < s < ∞ and of weak type (H, L).

In this paper we construct a special sort of dilation for an arbitrary polynomially bounded operator. This enables us to show that the problem whether every polynomially bounded operator is similar to a contraction can be reduced to a subclass of it.

For an operator bimodule X over von Neumann algebras A ⊆ B(H) and B ⊆ B(K), the space of all completely bounded A, B-bimodule maps from X into B(K,H), is the bimodule dual of X. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To X a normal operator bimodule Xn is associated so that completely bounded A, B-bimodule maps from...

In this paper, we explore what happens when the same techniques are applied to the problem of estimating eigenvalues of the adjacency operator on finite graphs of bounded degree. In Theorem 7, we show how eigenvalues of the adjacency operator on a finite graph Γ may be bounded in terms of the biggest eigenvalues of the adjacency operator on “geodesic balls” in Γ. We find explicit bounds for the...