منابع مشابه
Almost multiplicative linear functionals and approximate spectrum
We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...
متن کاملalmost multiplicative linear functionals and approximate spectrum
we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...
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In this paper, we study some kinds of majorizations on $textbf{M}_{n}$ and their linear or strong linear preservers. Also, we find the structure of linear or strong linear preservers which are multiplicative, i.e. linear or strong linear preservers like $Phi $ with the property $Phi (AB)=Phi (A)Phi (B)$ for every $A,Bin textbf{M}_{n}$.
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Let X be a compact Hausdorff space. We denote by C(X) the multiplicative semigroup of all continuous real-valued functions on X. Milgram [2] has shown that C(X) as a semigroup determines X. In this paper we investigate the set %(X) of all continuous positive nontrivial2 multiplicative functionals on C(X), where C(X) has the topology of uniform convergence. If multiplication is defined pointwise...
متن کاملSuperstability of Generalized Multiplicative Functionals
LetX be a set with a binary operation ◦ such that, for each x, y, z ∈ X, either x ◦y ◦z x ◦z ◦y, or z◦ x◦y x◦ z◦y . We show the superstability of the functional equation g x◦y g x g y . More explicitly, if ε ≥ 0 and f : X → C satisfies |f x ◦ y − f x f y | ≤ ε for each x, y ∈ X, then f x ◦ y f x f y for all x, y ∈ X, or |f x | ≤ 1 √1 4ε /2 for all x ∈ X. In the latter case, the constant 1 √ 1 4...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1973
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-28-2-251-253