Let B be a complex unital Banach algebra. We consider the Banach algebra A = B × C ordered by the algebra cone K = {(a, ξ) ∈ A : ‖a‖ ≤ ξ}, and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in B. 1. Ordered Banach algebras The aim of this paper is to stress the aspect of the applicability of the ordered Banach algebra...

Let F be a subfield of the field of real numbers and let Fn (n ≥ 2) be the n× n matrix algebra over F. It is shown that if Fn is a lattice-ordered algebra over F in which the identity matrix 1 is positive, then Fn is isomorphic to the lattice-ordered algebra Fn with the usual lattice order. In particular, Weinberg’s conjecture is true. Let L be a totally ordered field, and let Ln (n ≥ 2) be the...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...

in an earlier work we showed that for ordered fields f not isomorphic to the reals r, there are continuous 1-1 unctions on [0, 1]f which map some interior point to a boundary point of the image (and so are not open). here we show that over closed bounded intervals in the rationals q as well as in all non-archimedean ordered fields of countable cofinality, there are uniformly continuous 1-1 func...

Let 〈P,≤〉 be a partially ordered set. We define the poset Boolean algebra of P , and denote it by F (P ). The set of generators of F (P ) is {xp : p ∈ P}, and the set of relations is {xp ·xq = xp : p ≤ q}. We say that a Boolean algebra B is well-generated, if B has a sublattice G such that G generates B and 〈G,≤G〉 is well-founded. A wellgenerated algebra is superatomic. Theorem 1 Let 〈P,≤〉 be a...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

An incidence algebra of a nonlocally finite partially ordered set Q is a very rare concept, perhaps nonexistent. In this note, we will attempt to construct such an algebra. 1. Introduction. Let P be a partially ordered set (poset) and K a field of characteristic 0. The functions f : P × P → K, such that x y implies f (x,y) = 0, are called the incidence functions of P over K. The set of such fun...

We formulate Yang–Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of h̄) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum...

We consider and study Blaschke inductive limit algebras A(b), defined as inductive limits of disc algebras A(D) linked by a sequence b = {Bk}k=1 of finite Blaschke products. It is well known that big G-disc algebras AG over compact abelian groups G with ordered duals Γ = Ĝ ⊂Q can be expressed as Blaschke inductive limit algebras. Any Blaschke inductive limit algebraA(b) is a maximal and Dirichl...

In this paper we will present a new construction of any real geometric (Clifford) algebra $${\mathbb {G}}^{(p,q)}$$ with signature (p, q) where $$p+q=n$$ by defining product on the vector space {R}}^{(2^n)}$$ in manner similar to Gauss’ ordered pair complex numbers ( {C}}$$ ) and Hamilton’s quadruple quaternions {H}}$$ ). We motivate definition generalizing tuple multiplication each . Similar w...