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We give necessary and sufficient conditions for uniform exponential dichotomy of linear skew-product semiflows. We present connections between the uniform exponential dichotomy of a linear skew-product semiflow and the uniform admissibility of the pair (R,),Δ(R,)), where Δ(R,) denotes the unit ball in (R),).

The aim of this note is to give an extension of a result by McShane to a general stochastic integral operator with a non-Lipschitz condition on the coefficient functions.

The paper discusses properties of the characteristic determinant and the regularized trace associated to certain differential operators.

For an inclusion of the form , where (ℂ) is endowed with a state with diagonal weights λ = (λ, …, λ), we use Popa’s construction, for non-tracial states, to obtain an irreducible inclusion of factors, of index . () is identified with a subfactor inside the centralizer algebra of the canonical free product state on ⋆ (ℂ). Its structure is described by “infinite” semicircular elements as in {xc[32]}.

The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in [{xc4},∞) constructed in {xc[24]}, starting with the Jones’ subfactors inclusion , gt; 4. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.

If the weights correspond to a unitary, finite-dimensional representation of a Woronowicz’s compact quantum group , then the factor () is contained in the fixed point algebra of an action of the quantum group on ⋆ (ℂ), with equality if is (), (or (3) when = 2). By Takesaki duality, the factor (()) is Morita equivalent to ().

This method gives also another approach to find, as also recently proved in {xc[36]}, irreducible subfactors of () for index values bigger than 4.

We study the structure of some n-homogeneous *-algebras generated by flips. The algebra is generated by the flips , , , …, with the relations between the generators: = s, = s, s = ss, = ±1, = ±1, = ±1, 1 ≤ . The structure of such algebras generated by flips with the relations between generators was studied by Popovich, Samoilenko and Turowska. In the paper we prove that if such an algebra A is -homogeneous then it is trivial. Such an -homogeneous *-algebra is isomorphic to the algebra of all continuous matrix-functions of dimension over some compact subspace of the plane ℂ.

The aim of this paper is to study relations between “curved” conservative systems (systems for which the main operator is a function of contraction) and their transfer functions. We derive the boundedness property for such transfer functions and apply it to some problems of spectral analysis.

Let () be the normed algebra of all bounded linear operators : → , where is a normed space, and let be an operator ideal, so that () is a two-sided ideal in (). If is a tensor product of normed spaces, endowed with a tensor norm, an estimation is given for the distance of a tensor product operator Є() to () and it is applied to the study of the quasi-nilpotency of tensor product operators modulo ().

In {xc[17]}, it was shown that for every group Γ with a left-invariant metric such that (Γ, ) has bounded geometry, and which admits a uniform embedding into Hilbert space, the Baum-Connes assembly map with coefficients is split injective. In this paper, we strengthen this result by showing that Γ has a gamma element.

The main object of this paper is to discuss the problem of the uniform exponential stability and uniform observability of time-varying linear stochastic equations in Hilbert spaces. We give a representation of the covariance operator associated to the mild solutions of these equations which allow us to obtain a characterization of the uniform exponential stability of uniformly observable systems in terms of Lyapunov equations.

This is a historical survey that includes a progress report on the 1971 seminal paper of Pearcy and Topping and 32 years of subsequent investigations by a number of researchers culminating in a completely general characterization, for arbitrary ideal pairs, of their commutator ideal in terms of arithmetic means.

This characterization has applications to the study of generalized traces (linear functionals vanishing on the commutator ideal [()]) and to the study of the ()-ideal lattice and certain special sublattices. The structure of commutator ideals is essential for investigating traces which in turn is relevant for the calculation of the cyclic homology and the algebraic K-theory of operator ideals.