A note on the convolution in the Mellin sense with generalized functions.
A note on the differences of the consecutive powers of operators
We present two examples. One of an operator T such that is precompact in the operator norm and the spectrum of T on the unit circle consists of an infinite number of points accumulating at 1, and the other of an operator T such that is convergent to zero but T is not power bounded.
A note on the Dirichlet problem for the elliptic linear operator in Sobolev spaces with weight
A note on the distributional boundary values of analytic functions
A note on the extension of weak Radon measures on locally convex spaces to strong Radon measures
A note on the Hyers-Ulam problem
Let X,Y be real Banach spaces and ε > 0. Suppose that f:X → Y is a surjective map satisfying | ∥f(x)-f(y)∥ - ∥x-y∥ | ≤ ε for all x,y ∈ X. Hyers and Ulam asked whether there exists an isometry U and a constant K such that ∥f(x) - Ux∥ ≤ Kε for all x ∈ X. It is well-known that the answer to the Hyers-Ulam problem is positive and K = 2 is the best possible solution with assumption f(0) = U0 = 0. In this paper, using the idea of Figiel's theorem on nonsurjective isometries, we give a new proof of...
A Note on the Hyperstonian ßX.
A note on the isomorphic classification of spaces of continuous functions defined on intervals of ordinal numbers
A note on the joint spectrum in commutative Banach algebras
A note on the Köthe dual of Banach-valued echelon spaces.
A note on the lifting of linear and locally convex topologies on a quotient space.
A note on the modulus of -convexity and modulus of -convexity.
A note on the nonexistence of the Feynman integral
A note on the paper “Characterizations on 2-isometries”.
A note on the paper of Shütt "Unconditionality in tensor products''
A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld
It is proved that for any , where is the Poulsen simplex, so that and , are smooth points, there is a rotation of carrying in .
A note on the Poincaré inequality
The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.
A note on the predual of Lip(S, d)
A Note on the Raical of a Banach Algebra.
A note on the singular spectrum.
We compare the singular spectrum of a Banach algebra element with the usual spectrum and exponential spectrum.