Block Toeplitz operators with rational symbols and discrete singular systems
Abstract
This thesis concerns block Toeplitz operators (equations). Consider the block
Toeplitz operator T = [<I> k-j ]k,j=O' where the <I>k are complex m x m matrices such
that
00
(0.1)
v=-oo
The norm in (0.1) is the usual operator norm on an m x m matrix. The condition
(0.1) means that the symbol
00
( 0.2)
v=-oo
belongs t.o the Wiener class w mxm of all absolutely convergent sequences of complex
m x m matrices. Let 1 ~ p ~ oo be fixed. The block Toeplitz operator T induces a
bounded linear operator (also denoted by T) on l'';, namely,
00
(0.3) Yk = (Tx )k = L <I>k-vXv , k = 0, 1, 2, ... '
v=O
where x = (xo, x 1,X2, ... ) Et;.