Abstract
Some Properties of Algebra of Quotients with Bounded Evaluation of a Norm Ideal on Complex Banach Space
Highlights
Normalization of a subalgebra of Martindale of algebra of quotients of prime algebra was studied first in 1986 by Martin Mathieu in his thesis [8] by using ultraprime normed algebra which known as bounded algebra of quotients
In 2001, Cabrera-Mohammed extended the study of normalization of a subalgebra of Martindale of algebra of quotients of ultraprime normed algebra to totally prime algebra
In [3], Cabrera-Mohammed proved that the imbedding of a norm ideal on Hilbert space in algebra of quotients with bounded evaluation is continuous and the algebra of quotients with bounded evaluation is a right ideal of bounded algebra of quotients
Summary
Normalization of a subalgebra of Martindale of algebra of quotients of prime algebra was studied first in 1986 by Martin Mathieu in his thesis [8] by using ultraprime normed algebra which known as bounded algebra of quotients. Let A be a prime normed algebra, the right bounded algebra of quotients of A is defined to be subalgebra of Qr(A) Martindale algebra of quotients of A. Let q ∈ Qbr(A) the norm of Qbr(A) is given by ‖q‖r = inf{‖LIq‖: I ideal of A , qI ⊆ A, LIq is bounded} Qbr(A) it well be right bounded algebra of quotients for prime algebra A with identity by [8, proposition 2.6, p.
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