Summability Methods on Matrix Spaces

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Abstract
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.)

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