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Summability Methods on Matrix Spaces

Published online by Cambridge University Press:  20 November 2018

Josephine Mitchell
Josephine Mitchell*
Affiliation:
The Pennsylvania State University
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The matrix spaces under consideration are the four main types of irreducible bounded symmetric domains given by Cartan (5). Let z = (zjk) be a matrix of complex numbers, z' its transpose, z* its conjugate transpose and I = I(n) the identity matrix of order n. Then the first three types are defined by

(1)

where z is an n by m matrix (n ≤ m), a symmetric or a skew-symmetric matrix of order n (16). The fourth type is the set of complex spheres satisfying

(2)

where z is an n by 1 matrix. It is known that each of these domains possesses a distinguished boundary B which in the first three cases is given by

(3)

(In the case of skew symmetric matrices the distinguished boundary is given by (2) only if n is even.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 63 - 77
Copyright
Copyright © Canadian Mathematical Society 1961

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