King operators which preserve $x^j$

On Composition Operators Which Preserve Bmo

Q |f − fQ|dx < ∞, (1) where |Q| is the n-dimensional Lebesgue measure of Q, fQ = |Q|−1 ∫ Q fdx, and the supremum is taken over all closed cubes Q ⊂ D with sides parallel to the coordinate axes. Let D and D′ be subdomains of Rm and Rn, m, n ≥ 1, respectively. We say that a map F : D → D′ is measurable if F−1(E) is measurable for each measurable subset E of D′. We say that a measurable map F : D ...

Matricial Operators which Preserve Schauder Basis in p-Adic Analysis

In this work we give a generalization of the results established by W. Ruckle and L. W. Baric for the matrix transformations which preserve schauder basis in the classical case for a p-adic analysis. We give several characterizations of matricial operators which preserve Schauder bases in non archimedean Barrelled spaces. Mathematics Subject Classification: 46A35

Linear Operators Which Preserve Pairs on Which the Rank Is Additive

Let A and B be m n matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A + B) = rank(A) + rank(B) implies that rank(T (A) + T(B)) = rankT (A) + rankT (B). We characterize the set of all linear operators which preserve the set of pairs of n n matrices on which the rank is additive.

Mappings which preserve regular dodecahedrons

for all x, y ∈ X . A distance r > 0 is said to be preserved by a mapping f : X → Y if ‖ f (x)− f (y)‖ = r for all x, y ∈ X whenever ‖x− y‖ = r. If f is an isometry, then every distance r > 0 is preserved by f , and conversely. We can now raise a question whether each mapping that preserves certain distances is an isometry. Indeed, Aleksandrov [1] had raised a question whether a mapping f : X → ...

Operators on C(ω α ) which do not preserve C(ω α