منابع مشابه
On Completely Continuous Hankel Matrices1
1. Main theorem. Let x = (xo, xi, • • • ) be a sequence of complex numbers and let | x \ he the norm | x | = (^Z | x„ |2)1/2 2:0. Let an asterisk denote complex conjugation. If \x\ < <» and |y| < oo, let [x, y] = [y, x] denote the sum of the series ^T,xnyn, that is, the "scalar" product of y by x*. For a given x with a finite norm |x|, let x(t) denote a function of class i2(0, 27r) having the F...
متن کاملCompletely Continuous Banach Algebras
For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...
متن کاملCompletely continuous Banach algebras
For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...
متن کاملDeterminants of Hankel Matrices
The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.
متن کاملIrreducible Toeplitz and Hankel matrices
An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1958
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1958-0108684-8