A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper weâ€¦ (More)

A major obstacle in extending the theory of well-bounded operators to cover operators whose spectrum is not necessarily real has been the lack of a suitable variation norm applicable to functionsâ€¦ (More)

It is known that on a Hilbert space the sum of a well-bounded operator and a commuting real scalar-type spectral operator is well-bounded. It had been asked whether this may still hold for operatorsâ€¦ (More)

Every compact well-bounded operator has a representation as a linear combination of disjoint projections reminiscent of the representation of compact self-adjoint operators. In this note we show thatâ€¦ (More)

For 1 â‰¤ p < âˆž let Cp denote the usual von Neumann-Schatten ideal of compact operators on 2. The standard basis of Cp is a conditional one and so it is of interest to be able to identify the sets ofâ€¦ (More)

Motivated by problems in the spectral theory of linear operators the authors previously introduced a new concept of variation for functions defined on a nonempty compact subset of the plane. In thisâ€¦ (More)

This has a unique solution v(x, t) = Ttf(x) in the sense of Hille and Phillips [14, p. 622] whenever Tt is a C0â€“semigroup on X with generator âˆ’A; one writes Tt = eâˆ’tA [14, p. 321]. In order to ensureâ€¦ (More)

The nonlinear SchrÃ¶dinger equation NLSE(p, Î²), âˆ’iut = âˆ’uxx + Î²|u|pâˆ’2u = 0, arises from a Hamiltonian on infinite-dimensional phase space L2(T). For p â‰¤ 6, Bourgain (Comm. Math. Phys. 166 (1994),â€¦ (More)

AC-operators were introduced by Berkson and Gillespie as a generalization in the context of well-boundedness of normal operators on Hilbert space. In this paper we explore some of the properties ofâ€¦ (More)

Every finite metric tree has generalized roundness strictly greater than one. On the other hand, some countable metric trees have generalized roundness precisely one. The purpose of this paper is toâ€¦ (More)