On Some Transformations Related to Shift Transformations in Infinite Dyadic Product Spaces

Transformations on the Product of Grassmann Spaces

Let Gk denote the set of all k-dimensional subspaces of an n-dimensional vector space. We recall that two elements of Gk are called adjacent if their intersection has dimension k − 1. The set Gk is point set of a partial linear space, namely a Grassmann space for 1 < k < n − 1 (see Section 5) and a projective space for k ∈ {1, n − 1}. Two adjacent subspaces are—in the language of partial linear...

Entropy of infinite systems and transformations

The Kolmogorov-Sinai entropy is a far reaching dynamical generalization of Shannon entropy of information systems. This entropy works perfectly for probability measure preserving (p.m.p.) transformations. However, it is not useful when there is no finite invariant measure. There are certain successful extensions of the notion of entropy to infinite measure spaces, or transformations with ...

Transformations of measure on infinite-dimensional vector spaces∗

Some Sequence Spaces and Their Matrix Transformations

The most general linear operator to transform from new sequence space into another sequence space is actually given by an infinite matrix. In the present paper we represent some sequence spaces and give the characterization of (S (p), ) and (S (p), ).

Some Paranormed Sequence Spaces and Matrix Transformations

Let w, γ, γo, c, co and l∞ be the spaces of all, summable, summable to zero, convergent, null and bounded sequences respectively. The notion of statistical convergence of sequences was introduced by Fast [3], Schoenberg [12] and Buck [1] independently. Later on the idea was exploited from sequence space point of view and linked with summability by Fridy [4], S̆alát [11], Kolk [5], Rath and Tripa...