Subdifferentiability of Convex Functions with Values in an Ordered Vector Space.
Jochem Zowe (1974)
Mathematica Scandinavica
Lucas Jódar (1985)
Stochastica
Estudiamos la existencia de subespacios hiperinvariantes de operadores desplazamiento bilateral ponderados e invertibles definidos sobre un espacio de Hilbert con base ortogonal {en}, n perteneciendo a Z, por la expresión T en = wn en+1, donde las sucesiones {wn} y {w-n}, con n = 1, ..., ∞, son convergentes.
Béla Nagy (2013)
Studia Mathematica
Two characterizations of the reductivity of a cyclic normal operator in Hilbert space are proved: the equality of the sets of cyclic and *-cyclic vectors, and the equality L²(μ) = P²(μ) for every measure μ equivalent to the scalar-valued spectral measure of the operator. A cyclic subnormal operator is reductive if and only if the first condition is satisfied. Several consequences are also presented.
Dmitry V. Yakubovich (1998)
Revista Matemática Iberoamericana
Xia proves in [9] that a pure subnormal operator S is completely determined by its self-commutator C = S*S - SS*, restricted to the closure M of its range and the operator Λ = (S*|M)*. In [9], [10], [11] he constructs a model for S that involves this two operators and the so-called mosaic, which is a projection-valued function, analytic outside the spectrum of the minimal normal extension of S. He finds all pure subnormals S with rank C = 2. We will give a complete description of pairs of matrices...
Dmitry V. Yakubovich (1998)
Revista Matemática Iberoamericana
This paper concerns pure subnormal operators with finite rank self-commutator, which we call subnormal operators of finite type. We analyze Xia's theory of these operators [21]-[23] and give its alternative exposition. Our exposition is based on the explicit use of a certain algebraic curve in C2, which we call the discriminant curve of a subnormal operator, and the approach of dual analytic similarity models of [26]. We give a complete structure result for subnormal operators of finite type, which...
K. Rudol (1997)
Banach Center Publications
Alexandru Aleman (1996)
Manuscripta mathematica
Franciszek Hugon Szafraniec (2005)
Banach Center Publications
For an unbounded operator S the question whether its subnormality can be built up from that of every , the restriction of S to a cyclic space generated by f in the domain of S, is analyzed. Though the question at large has been left open some partial results are presented and a possible way to prove it is suggested as well.
Franciszek Hugon Szafraniec (2007)
Banach Center Publications
Franciszek Hugon Szafraniec (2007)
Banach Center Publications
Duggal, B.P. (2005)
International Journal of Mathematics and Mathematical Sciences
Angelo Favini (1971)
Rendiconti del Seminario Matematico della Università di Padova
Constanza Borelli Forti, István Fenyö (1980)
Stochastica
Let X be an arbitrary Abelian group and E a Banach space. We consider the difference-operators ∆n defined by induction:(∆f)(x;y) = f(x+y) - f(x), (∆nf)(x;y1,...,yn) = (∆n-1(∆f)(.;y1)) (x;y2,...,yn)(n = 2,3,4,..., ∆1=∆, x,yi belonging to X, i = 1,2,...,n; f: X --> E).Considering the difference equation (∆nf)(x;y1,y2,...,yn) = d(x;y1,y2,...,yn) with independent variable increments, the most general solution is given explicitly if d: X x Xn --> E is a given bounded function. Also the...
Jin-Hsien Wang, Pei Wu (1991)
Studia Mathematica
B. R. Choe, H. Koo, Y. J. Lee (2008)
Revista Matemática Iberoamericana
Tosio Kato (1982)
Mathematische Zeitschrift
Egor Alekhno (2012)
Open Mathematics
We study the superposition operator f on on the space ac 0 of sequences almost converging to zero. Conditions are derived for which f has a representation of the form f x = a+bx +g x, for all x ∈ ac 0 with a = f 0, b ∈ D(ac 0), g a superposition operator from ℓ∞ into I(ac 0), D(ac 0) = {z: zx ∈ ac 0 for all x ∈ ac 0}, and I(ac 0) the maximal ideal in ac 0. If f is generated by a function f of a real variable, then f is linear. We consider the conditions for which a bounded function f generates f...
Vodopyanov, S.K., Ukhlov, A.D. (2002)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
Supama, Darmawijaya, Soeparna (2004)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
Cao, Huai-Xin, Lv, Ji-Rong, Rassias, John Michael (2009)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]