The single valued extension property dates back to the early days of local spectral theory; see the recent monograph of Laursen and Neumann [10] or Aiena [11].
Let T ∈ B ( H ) be k-quasi-∗-class A. Then T satisfies Bishop's property, the single valued extension property and the Dunford property (C).
We say that an operator T has the single valued extension property at λ (abbreviated SVEP at λ) if for every open set U containing λ the only analytic function f : U → H which satisfies the equation ( T - λ ) f = 0. is the constant function f ≡ 0 on U. T has SVEP if T has SVEP at every point λ ∈ ℂ. Definition 1.1.
Definition 1.1 An operator T ∈ B ( H ) is said to have the single valued extension property (SVEP) at λ ∈ C if for every open neighborhood G of λ, the only function f ∈ H ( G ) such that ( T − μ ) f = 0 on G is 0 ∈ H ( G ), where H G G ) means the space of all analytic functions on G.
A bounded operator T ∈ B ( X ) is said to have the single valued extension property (abbreviated SVEP) if, for every open subset G of ℂ and any analytic function f : G → X such that ( T − z ) f ( z ) ≡ 0 on G, we have f ( z ) ≡ 0 on G.
We say that T has the single valued extension property (abbreviated SVEP if, for every open set U of ℂ, the only analytic solution f: U → H of the equation ( T − λ ) f = 0 for all λ ∈ U. is a zero function on U. Theorem 3.5 Let T be an algebraically k-quasi-M-hyponormal operator.
We invent the new notion of coordinatewise multiple summing operators in Banach spaces, and use it to study various vector valued extensions of the well-know Bohnenblust Hille inequality (which originally extended Littlewood's 4/3-inequality).
2.4 Courses-of-Values, Extensions, and Proposed Mathematical Foundations 2.4.1 Courses-of-Values and Extensions Frege's ontology consisted of two fundamentally different types of entities, namely, functions and objects (1891, 1892b, 1904).
It is demonstrated that there is a critical value of extension rate at which the beam loses stability in the case when the base is fixed.
So to measure how much people value life extension, he and Topel found examples of what people actually spent, often in roundabout ways, to lengthen their own lives.
