Let A,B be bounded operators on complex Banach spaces X and Y respectively. The tensor product X (?)_α Y denotes the completion of X(?)Y with respect to a quasi-uniform reasonable norm α. In the case X and Y are Hil...Let A,B be bounded operators on complex Banach spaces X and Y respectively. The tensor product X (?)_α Y denotes the completion of X(?)Y with respect to a quasi-uniform reasonable norm α. In the case X and Y are Hilbert spaces, Brown and Percy showed that σ(A(?)B)-σ(A)(?)σ(B). This work was generalized by Scheter and Dash, and it was further generalized by R. Harte. He computed the joint spectrum for certain system of elements in a tensor product of Banach algebras.展开更多
文摘Let A,B be bounded operators on complex Banach spaces X and Y respectively. The tensor product X (?)_α Y denotes the completion of X(?)Y with respect to a quasi-uniform reasonable norm α. In the case X and Y are Hilbert spaces, Brown and Percy showed that σ(A(?)B)-σ(A)(?)σ(B). This work was generalized by Scheter and Dash, and it was further generalized by R. Harte. He computed the joint spectrum for certain system of elements in a tensor product of Banach algebras.
