Abstract
We generalize (in two natural ways) the C*-algebra generated by matrices of bounded operators in a separable Hilbert space H with a bounded number of nonzero elements in each row and each column, introduced recently by V. Manuilov. We consider the standard C*-Hilbert module HA instead of H = Hℂ. Also we consider the algebras with finiteness conditions only on rows or only on columns. For related general linear groups, we prove the contractibility (Kuiper type theorems) and some other properties.
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