Weknow that not all minimal projections inLp (1<p<∞) are unique (see [B. Shekhtman, L. Skrzypek, On the non-uniqueness ofminimal projections inLp spaces]).The aimof this paper is examine the connection of the Chalmers–Metcalf operator (introduced in [B.L. Chalmers, F.T. Metcalf, A characterization and equations for minimal projections and extensions, J. Oper. Theory 32 (1994) 31–46]) to the uni...

∇XV = λX for every vector field X. (1.2) Here ∇ denotes the Levi-Civita connection of g. We call vector fields satisfying (1.2) closed conformal vector fields. They appear in the work of Fialkow [3] about conformal geodesics, in the works of Yano [7–11] about concircular geometry in Riemannian manifolds, and in the works of Tashiro [6], Kerbrat [4], Kühnel and Rademacher [5], and many other aut...

A theory has been developed to calculate the Rademacher-Walsh t ransform f rom a cube a r r a y specification of incompletely specified Boolean functions. T h e importance of representing Boolean functions a s a r r a y s of disjoint ONa n d Ix-cubes has been pointed out , a n d a n efficient new algori thm to generate disjoint cubes f rom nondisjoint ones has been designed. The t r ans fo rm a...

For an R-bounded families of operators on L1 we associate a family of representing measures and show that they form a weakly compact set. We consider a sectorial operator A which generates an R-bounded semigroup on L1. We show that given 2 > 0 there is an invertible operator U : L1 → L1 with ‖U − I‖ < 2 such that for some positive Borel function w we have U(D(A)) ⊃ L1(w).

We introduce the notion of scaled Enflo type of a metric space, and show that for Banach spaces, scaled Enflo type p is equivalent to Rademacher type p.

Let’s first see how primitive covers were inadequate. Recall that a function class G is a primitive cover for a function class F at scale > 0 over some set S if: • G ⊆ F , • |G| <∞, and • for every f ∈ F there exists g ∈ G with supx∈S |g(x)− f(x)| ≤ . Last class, we gave a generalization bound for classes with primitive covers (basically, primitive covers give discretizations, and then we apply...