What is the name of this algebra?

The well-known Wiener algebra is the set of complex-valued functions:

f(t) = Sum_{n =-infinty}{infinity} t^n a_n,

where t is on the unit circle and the sequence of numbers {a_n} is
absolutely summable.

A natural extension of this for some problems I am working on is the
set of matrix-valued, complex functions:

f(t) = Sum_{n =-infinity}{infinity} t^n A_n,

where t is on the unit circle, but now the A_n are *each* N x N matrices, N
fixed and finite.
Assume that Sum_{n =-infinty}{infinity} || A_n || < infinity, where || A ||
is a matrix norm.
Then, these functions f(t) form a normed non-commutative algebra, call it B,
using
natural (matrix) addition and multiplication, and with
B-norm || f || = Sum_{n =-infinity}{infinity} || A_n ||.
In this last expression, the norm on the left is the B-norm and
the norm inside the sum on the right is the matrix norm.

I assume this algebra is well-studied somewhere. What is the name of it?

thanks,
alan



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