An example of a nonseparable Banach algebra without nonseparable commutative subalgebras
We present an example of an algebra that is generated by elements, and cannot be made a topological algebra. This answers a problem posed by W. Żelazko.
We show that for every there exists a weight such that the Lorentz Gamma space is reflexive, its lower Boyd and Zippin indices are equal to zero and its upper Boyd and Zippin indices are equal to one. As a consequence, the Hardy-Littlewood maximal operator is unbounded on the constructed reflexive space and on its associate space .
We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
When dealing with interpolation spaces by real methods one is lead to compute (or at least to estimate) the K-functional associated to the couple of interpolation spaces. This concept was first introduced by J. Peetre (see [8], [9]) and some efforts have been done to find explicit expressions of it for the case of Lebesgue spaces. It is well known that for the couple consisting of L1 and L∞ on [0, ∞) K is given by K (t; f, L1, L∞) = ∫0t f* where f* denotes the non increasing rearrangement of the...