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ON SOME INEQUALITIES IN *NORMED* *ALGEBRAS*

, 2007

"... ABSTRACT. Some inequalities in normed algebras that provides lower and upper bounds for the norm of ∑n j=1 ajxj are obtained. Applications for estimating the quantities ∥ ∥ −1 x ∥ ∥ x ± ∥y−1 ∥ ∥ y and ∥ ∥ ∥y−1∥ ∥ x ± ∥ ∥x−1∥ ∥ y ∥ for invertible elements x, y in unital normed algebras are also ..."

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ABSTRACT. Some inequalities in

*normed**algebras*that provides lower and upper bounds for the*norm*of ∑n j=1 ajxj are obtained. Applications for estimating the quantities ∥ ∥ −1 x ∥ ∥ x ± ∥y−1 ∥ ∥ y and ∥ ∥ ∥y−1∥ ∥ x ± ∥ ∥x−1∥ ∥ y ∥ for invertible elements x, y in unital*normed**algebras*are also###
*Normed* *algebras* with involution

"... abstract: We show that most of the theory of Hermitian Banach algebras can be proved for normed ∗-algebras without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x ∗ x) 1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is ..."

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abstract: We show that most of the theory of Hermitian Banach

*algebras*can be proved for*normed*∗-*algebras*without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x ∗ x) 1/2 is the Pták function), which is essential in the theory of Hermitian Banach*algebras*###
Multihomogeneous *Normed* *Algebras* and Polynomial Identities

"... Abstract In this paper we consider PI-algebras A over R or C. It is well known that in general such algebras are not normed algebras. In fact, there is a nilpontent commutative algebra which is not a normed algebra, see ..."

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Abstract In this paper we consider PI-

*algebras*A over R or C. It is well known that in general such*algebras*are not*normed**algebras*. In fact, there is a nilpontent commutative*algebra*which is not a*normed**algebra*, see###
*Algebraic* Extensions of *Normed* *Algebras*

, 2000

"... Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author’s. ..."

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Disclaimer: This dissertation does not contain plagiarised material; except where otherwise stated all theorems are the author’s.

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Generated by t-*norm* *Algebras*

"... Abstract. In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continuous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another pro ..."

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Abstract. In this paper we show that the subvarieties of BL, the variety of BL-

*algebras*, generated by single BL-chains on [0, 1], determined by continuous t-*norms*, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another###
Notes on *normed* *algebras*, 4

, 2004

"... Let A be a finite-dimensional algebra over the complex numbers with nonzero identity element e. If x ∈ A, then the resolvent set associated to x is the set ρ(x) of complex numbers λ such that λ e − x is invertible, and the spectrum of x is the set σ(x) of complex numbers λ such that λ e − x is not i ..."

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Let A be a finite-dimensional

*algebra*over the complex numbers with nonzero identity element e. If x ∈ A, then the resolvent set associated to x is the set ρ(x) of complex numbers λ such that λ e − x is invertible, and the spectrum of x is the set σ(x) of complex numbers λ such that λ e − x###
Notes on *normed* *algebras*, 2

, 2004

"... Let A be a finite-dimensional commutative algebra over the complex numbers, with identity element e. Thus A is a finite-dimensional complex vector space equipped with an additional binary operation of multiplication which satisfies the usual rules of associativity, commutativity, and distributivity, ..."

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Let A be a finite-dimensional commutative

*algebra*over the complex numbers, with identity element e. Thus A is a finite-dimensional complex vector space equipped with an additional binary operation of multiplication which satisfies the usual rules of associativity, commutativity, and distributivity###
Notes on *normed* *algebras*, 5

, 2004

"... Let A be a finite-dimensional commutative algebra over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the algebra of complex-valued functions on M, with respect to point ..."

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Let A be a finite-dimensional commutative

*algebra*over the complex numbers with nonzero multiplicative identity element e. Let M denote the set of homomorphisms from A onto the complex numbers. Thus we get a homomorphism from A into the*algebra*of complex-valued functions on M, with respect###
Notes on *normed* *algebras*

, 2004

"... All vector spaces and so forth here will be defined over the complex numbers. If z = x+i y is a complex number, where x, y are real numbers, then the complex conjugate of z is denoted z and defined to be x − i y. The complex conjugate of a sum or product of complex numbers is equal to the correspond ..."

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that the modulus of a sum of two complex numbers is less than or equal to the sum of the moduli of the complex numbers. By a finite-dimensional

*algebra*we mean a finite dimensional complex vector space A equipped with a binary operation which satisfies the usual associativity and distributivity properties###
Notes on *normed* *algebras*, 3

, 2004

"... Let A be a countably-infinite commutative semigroup with an identity element 0. Thus A is equipped with a binary operation + which is commutative and associative, and x + 0 = x for all x ∈ A. If f1, f2 are two complex-valued functions on A, then we can try to define the convolution of f1, f2 by (1) ..."

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attention to functions with finite support, then we get a nice commutative

*algebra*. For each a ∈ A define δa to be the function on A which is equal to 1 at a