CONCEPT, PRINCIPLE, AND NORM—EQUALITY BEFORE THE LAW RECONSIDERED

ABSTRACTDespite the attention equality before the law has received, both laudatory and critical, peculiarly little has been done to precisely define it. The first ambition of this paper is to remedy this, by exploring the various ways in which a principle of equality before the law can be understood and suggest a concise definition. With a clearer understanding of the principle in hand we are better equipped to assess traditional critique of the principle. Doing so is the second ambition of this paper. I will argue that traditional criticisms are unpersuasive, but that there is a different, powerful argument against equality before the law. The third ambition of the paper is to argue that there is a sense, overlooked by both proponents and critics, in which the principle still captures something important, albeit at the cost of shifting from intrinsic to instrumental value.

Commutator and self-commutator approximants II

We minimize the quantities (i) ||T -(AX-X A) ||, (ii) ||T -(X*X-XX*)|| and (iii) ||T -(AX - X B)|| where T is isometric and where in (i) A is paranormal and commutes with T , in (ii) X*(or X ) is paranormal and commutes with T , and in (iii) A and B are paranormal and AT = T B and T A = BT. The upshot is that these quantities are minimized when 0 = AX - XA = X*X - XX*= AX - XB. To prove these results we obtain the power norm equality for paranormal operators: if A is paranormal then ||An|| = ||A||n if n?N.

On the Modulii of Analytic Functions

The problem to be considered in this note, in its most concrete form, is the determination of all quartets f1, f2, g1, g2 of functions analytic on some domain and satisfying*where p > 0. When p = 2 the question can be reformulated in terms of finding a necessary and sufficient condition for (two-dimensional) Hilbert space valued analytic functions to have equal pointwise norms, and the answer (Theorem 1) justifies this point of view. If p ≠ 2, the problem is solved by reducing to the case p = 2, and the reformulation in terms of the norm equality of lp valued analytic functions gives no clue to the answer.