Explicit constructions of dense common hypercyclic subspaces
نویسندگان
چکیده
منابع مشابه
Operators with Common Hypercyclic Subspaces
We provide a reasonable sufficient condition for a family of operators to have a common hypercyclic subspace. We also extend a result of the third author and A. Montes [22], thereby obtaining a common hypercyclic subspace for certain countable families of compact perturbations of operators of norm no larger than one.
متن کاملDense Testers: Almost Linear Time and Locally Explicit Constructions
We develop a new notion called (1− ǫ)-tester for a set M of functions f : A → C. A (1− ǫ)-tester for M maps each element a ∈ A to a finite number of elements Ba = {b1, . . . , bt} ⊂ B in a smaller sub-domain B ⊂ A where for every f ∈ M if f(a) 6= 0 then f(b) 6= 0 for at least (1 − ǫ) fraction of the elements b of Ba. I.e., if f(a) 6= 0 then Prb∈Ba [f(b) 6= 0] ≥ 1− ǫ. The size of the (1− ǫ)-test...
متن کاملCommon Hypercyclic Vectors for Families of Operators
We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators, which is based on a previous one given by Costakis and Sambarino. As an application, we get common hypercyclic vectors for a particular family of hypercyclic scalar multiples of the adjoint of a multiplier in the Hardy space, generalizing recent results by...
متن کاملMaximally monotone linear subspace extensions of monotone subspaces: explicit constructions and characterizations
Monotone linear relations play important roles in variational inequality problems and quadratic optimizations. In this paper, we give explicit maximally monotone linear subspace extensions of a monotone linear relation in finite dimensional spaces. Examples are provided to illustrate our extensions.Our results generalize a recent result by Crouzeix and Ocaña-Anaya.
متن کاملCommon Hypercyclic Vectors for Composition Operators
A continuous operator acting on a topological vector space X is called hypercyclic provided there exists a vector x ∈ X such that its orbit {T nx; n ≥ 1} is dense in X. Such a vector is called a hypercyclic vector for T . The set of hypercyclic vectors will be denoted by HC(T ). The first example of hypercyclic operator was given by Birkhoff, 1929 [3], who shows that the operator of translation...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 2007
ISSN: 0034-5318
DOI: 10.2977/prims/1201011786