منابع مشابه
On Commuting U-operators in Jordan Algebras
Recently J.A.Anquela, T.Cortés, and H.Petersson [2] proved that for elements x, y in a non-degenerate Jordan algebra J , the relation x ◦ y = 0 implies that the U -operators of x and y commute: UxUy = UyUx. We show that the result may be not true without the assumption on nondegeneracity of J . We give also a more simple proof of the mentioned result in the case of linear Jordan algebras, that ...
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We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these co...
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Any linear transformation can be represented by its matrix representation. In an ideal situation, all linear operators can be represented by a diagonal matrix. However, in the real world, there exist many linear operators that are not diagonalizable. This gives rise to the need for developing a system to provide a beautiful matrix representation for a linear operator that is not diagonalizable....
متن کاملNorms and CB Norms of Jordan Elementary Operators
We establish lower bounds for norms and CB-norms of elementary operators on B(H). Our main result concerns the operator Ta,bx = axb + bxa and we show ‖Ta,b‖ ≥ ‖a‖‖b‖, proving a conjecture of M. Mathieu. We also establish some other results and formulae for ‖Ta,b‖cb and ‖Ta,b‖ for special cases. Our results are related to a problem of M. Mathieu [13, 14] asking whether ‖Ta,b‖ ≥ c‖a‖‖b‖ holds in ...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 2001
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s001708950103004x