For a, α > 0 let E(a, α) be the set of all compact operators A on a separable Hilbert space such that sn(A) = O(exp(−anα)), where sn(A) denotes the n-th singular number of A. We provide upper bounds for the norm of the resolvent (zI − A) of A in terms of a quantity describing the departure from normality of A and the distance of z to the spectrum of A. As a consequence we obtain upper bounds fo...

Jayne and Rogers proved that every function from an analytic space into a separable metrizable space is decomposable into countably many continuous functions with closed domains if and only if the preimage of each Fσ set under it is again Fσ . Many researchers conjectured that the JayneRogers theorem can be generalized to all finite levels of Borel functions. In this paper, by using the Shore-S...

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space X. In particular we give an example of a reflexive X so that all spreading models of X contain l1 but none of them is isomorphic to l1. We also prove that for any countable set C of spreading models generated by weakly null sequences there is a spreading model generat...

Let H be a separable Hilbert space. Given two strongly commuting CP0-semigroups φ and θ on B(H), there is a Hilbert space K ⊇ H and two (strongly) commuting E0-semigroups α and β such that φs ◦ θt(PHAPH) = PHαs ◦ βt(A)PH for all s, t ≥ 0 and all A ∈ B(K). In this note we prove that if φ is not an automorphism semigroup then α is cocycle conjugate to the minimal ∗-endomorphic dilation of φ, and ...

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for 2 × 2 and 2× 3 systems. Here, the positivity of the partial transposition of a state is necessary and sufficient for its separability. However, it is not the case in general. Some examples of mixtures which demonstrate the utility of the criterion are con...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

Let E be a Banach space with a separable dual. Zippin’s theorem asserts that E embeds in a Banach space E1 with a shrinking basis, and W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński have shown that E is a quotient of a Banach space E2 with a shrinking basis. These two results use the interpolation theorem established by W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński. Here, we ...