Random linear functionals
نویسندگان
چکیده
منابع مشابه
Linear Functionals of Eigenvalues of Random Matrices
LetMn be a random n n unitary matrix with distribution given by Haar measure on the unitary group. Using explicit moment calculations, a general criterion is given for linear combinations of traces of powers of Mn to converge to a Gaussian limit as n ! 1. By Fourier analysis, this result leads to central limit theorems for the measure on the circle that places a unit mass at each of the eigenva...
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We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...
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It is shown that a linear functional on a space of functions can be described by G, a group of its symmetries, together with the restriction of to certain G-invariant functions. This simple consequence of invariant theory has long been used, implicitly, in the construction of numerical integration rules. It is the author's hope that, by showing that these ideas have nothing to do with the origi...
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Given a set of points in Euclidean space, we say that two linear functionals diier on that set if they give rise to diierent linear orderings of the points. We investigate what the largest and smallest number of diierent linear functionals can be as a function of the number of points and the dimension of the space. 1. Introduction The purpose of this paper is to investigate the number of diiere...
متن کاملalmost multiplicative linear functionals and approximate spectrum
we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1969-0264726-2