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Algebras of quotients with bounded evaluation of a normed semiprime algebra

100%

Cabrera M., Mohammed A.

Studia Mathematica

2003

tom 154

nr 2

113-135

We deal with the algebras consisting of the quotients that produce bounded evaluation on suitable ideals of the multiplication algebra of a normed semiprime algebra A. These algebras of quotients, which contain A, are subalgebras of the bounded algebras of quotients of A, and they have an algebra seminorm for which the relevant inclusions are continuous. We compute these algebras of quotients for some norm ideals on a Hilbert space H: 1) the algebras of quotients with bounded evaluation of the ideal of all compact operators on H are equal to the Banach algebra of all bounded linear operators on H, 2) the algebras of quotients with bounded evaluation of the Schatten p-ideal on H (for 1 ≤ p<∞) are equal to the Schatten p-ideal on H. We also prove that the algebras of quotients with bounded evaluation on the class of totally prime algebras have an analytic behavior similar to the one known for the bounded algebras of quotients on the class of ultraprime algebras.

Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras

81%

Brešar M., Cabrera M., Fošner M., Villena A.

Studia Mathematica

2005

tom 169

nr 3

207-228

A linear subspace M of a Jordan algebra J is said to be a Lie triple ideal of J if [M,J,J] ⊆ M, where [·,·,·] denotes the associator. We show that every Lie triple ideal M of a nondegenerate Jordan algebra J is either contained in the center of J or contains the nonzero Lie triple ideal [U,J,J], where U is the ideal of J generated by [M,M,M]. Let H be a Jordan algebra, let J be a prime nondegenerate Jordan algebra with extended centroid C and unital central closure Ĵ, and let Φ: H → J be a Lie triple epimorphism (i.e. a linear surjection preserving associators). Assume that deg(J) ≥ 12. Then we show that there exist a homomorphism Ψ: H → Ĵ and a linear map τ: H → C satisfying τ([H,H,H]) = 0 such that either Φ = Ψ + τ or Φ = -Ψ + τ. Using the preceding results we show that the separating space of a Lie triple epimorphism between Jordan-Banach algebras H and J lies in the center modulo the radical of J.

Ograniczanie wyników

2 Studia Mathematica

2 Cabrera M.

1 Brešar M.

1 Fošner M.

1 Mohammed A.

1 Villena A.

1 2005

1 2003

Wyniki wyszukiwania

Algebras of quotients with bounded evaluation of a normed semiprime algebra

Lie triple ideals and Lie triple epimorphisms on Jordan and Jordan-Banach algebras