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In this article, we exhibit a large class of Banach spaces whose open unit balls are bounded symmetric homogeneous domains. These Banach spaces, which we call J*-algebras, are linear spaces of operators mapping one Hilbert space into another and have a kind of Jordan tripte product structure. In particular, all Hilbert spaces and all B*--algebras are… (More)

Let X and Y be real normed linear spaces and let φ : X → R be a non-negative function satisfying φ(x+ y) ≤ φ(x) + ‖y‖ for all x, y ∈ X. We show that there exist optimal constants cm,k such that if P : X → Y is any polynomial satisfying ‖P (x)‖ ≤ φ(x)m for all x ∈ X, then ‖D̂kP (x)‖ ≤ cm,kφ(x) whenever x ∈ X and 0 ≤ k ≤ m. We obtain estimates for these… (More)

0. Introduction Our object is to study domains which are the region of negative definiteness of an operator-valued Hermitian form defined on a space of operators and to investigate the biholomorphic linear fractional transformations between them. This is a unified setting in which to consider operator balls, operator half-planes, strictly J-contractive… (More)

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents… (More)

- Lawrence A. Harris, Lawrence E. Harris, Fred V. Keenan
- 1999

In the second half of year 2,000, the U.S. equity and options markets will switch to decimal pricing. Following the switch, and barring regulatory intervention, competition will likely drive the minimum price increment (tick size) down to a penny. This paper surveys the effects that trading on pennies will have on investors, dealers, brokers, exchanges, and… (More)

This article considers the extension of V. A. Markov’s theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain… (More)

The Hille-Yosida and Lumer-Phillips theorems play an important role in the theory of linear operators and its applications to evolution equations, probability and ergodic theory. (See, for example, [17] and [9].) Different nonlinear generalizations and analogues of these theorems can be found, for instance, in [13] and [2]. We are interested in establishing… (More)

We discuss Lagrange interpolation on two sets of nodes in two dimensions where the coordinates of the nodes are Chebyshev points having either the same or opposite parity. We use a formula of Xu for Lagrange polynomials to obtain a general interpolation theorem for bivariate polynomials at either set of Chebyshev nodes. An extra term must be added to the… (More)

- Lawrence A. Harris
- Proceedings of the National Academy of Sciences…
- 1969

In this paper we show that any Fréchet holomorphic function mapping the open unit ball of one normed linear space into the closed unit ball of another must be a linear mapping if the Fréchet derivative of the function at zero is a surjective isometry. From this fact we deduce a Banach-Stone theorem for operator algebras which generalizes that of R. V.… (More)

This expository article shows how classical inequalities for the derivative of polynomials can be proved in real and complex Hilbert spaces using only elementary arguments from functional analysis. As we shall see, there is a surprising interconnection between an equality of norms for symmetric multilinear mappings due to Banach and an inequality for the… (More)