Wyniki wyszukiwania

1

On the joint spectral radius of commuting matrices

100%

Bhatia R., Вhattacharyya T.

Studia Mathematica

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1995

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tom 114

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nr 1

29-38

EN

For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.

2

Perturbation theorems for Hermitian elements in Banach algebras

100%

Bhatia R., Drissi D.

Studia Mathematica

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1999

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tom 134

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nr 2

111-117

EN

Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.

3

Maps on matrices that preserve the spectral radius distance

81%

Bhatia R., Šemrl P., Sourour A. R.

Studia Mathematica

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1999

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tom 134

|

nr 2

99-110

EN

Let ϕ be a surjective map on the space of n×n complex matrices such that r(ϕ(A)-ϕ(B))=r(A-B) for all A,B, where r(X) is the spectral radius of X. We show that ϕ must be a composition of five types of maps: translation, multiplication by a scalar of modulus one, complex conjugation, taking transpose and (simultaneous) similarity. In particular, ϕ is real linear up to a translation.

Ograniczanie wyników

3 Studia Mathematica

3 Bhatia R.

1 Drissi D.

1 Sourour A. R.

1 Šemrl P.

1 Вhattacharyya T.

2 1999

1 1995

On the joint spectral radius of commuting matrices

Perturbation theorems for Hermitian elements in Banach algebras

Maps on matrices that preserve the spectral radius distance