The regularity of convolution and restriction of distributions
The regularity of the positive part of functions in with applications to parabolic equations
Let with be given. Then we show by means of a counter-example that the positive part of has less regularity, in particular it holds in general. Nevertheless, satisfies an integration-by-parts formula, which can be used to prove non-negativity of weak solutions of parabolic equations.
The relative Dixmier property for inclusions of von Neumann algebras of finite index
The Relative Spectrum of Elements in a Real Banach Algebra.
The Rényi distances of Gaussian measures
The author in the paper evaluates the Rényi distances between two Gaussian measures using properties of nuclear operators and expresses the formula for the asymptotic rate of the Rényi distances of stationary Gaussian measures by the corresponding spectral density functions in a general case.
The Rohlin property for automorphisms of UHF algebras.
The role of Onofri type inequalities in the symmetry properties of extremals for Caffarelli-Kohn-Nirenberg inequalities, in two space dimensions
We first discuss a class of inequalities of Onofri type depending on a parameter, in the two-dimensional Euclidean space. The inequality holds for radial functions if the parameter is larger than . Without symmetry assumption, it holds if and only if the parameter is in the interval . The inequality gives us some insight on the symmetry breaking phenomenon for the extremal functions of the Caffarelli-Kohn-Nirenberg inequality, in two space dimensions. In fact, for suitable sets of parameters (asymptotically...
The Schroeder-Bernstein index for Banach spaces
In relation to some Banach spaces recently constructed by W. T. Gowers and B. Maurey, we introduce the notion of Schroeder-Bernstein index SBi(X) for every Banach space X. This index is related to complemented subspaces of X which contain some complemented copy of X. Then we establish the existence of a Banach space E which is not isomorphic to Eⁿ for every n ∈ ℕ, n ≥ 2, but has a complemented subspace isomorphic to E². In particular, SBi(E) is uncountable. The construction of E follows the approach...
The Schur multiplication in tensor algebras
The S...-criterion for Hankel forms on the Fock space, 0 < p < 1.
The second conjugate algebras of Banach algebras.
The second dual spaces of the sets of -strongly convergent and bounded sequences.
The semi- property for normed Riesz spaces
The Semi Orlicz Space
The semi-difference entire sequence space .
The semigroup of Fredholm operators.
The separated extensional Chu category.
The sequential approach to the product of distribution.
The set of automorphisms of B(H) is topologically reflexive in B(B(H))
The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence of automorphisms of B(H) (depending on A) such that . Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
The set of exponents for isomorphic extensions of Hölder maps is not always closed.