An invitation to operator theory

By Y. Abramovich, Charalambos D. Aliprantis. 2002

650 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/309080d2525e5b860bd64e60fa17e0fcce4fafef

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In Computational Theory and Mathematics

Citations in the corpus

Semiclassical non-concentration near hyperbolic orbits (2006, methodology): “L2-Betti numbers of configuration spaces with Poisson and Lebesgue–Poisson measures, were computed in [2,15], respectively (see also [1,14,16]).”
Operator spaces with few completely bounded maps (2004, methodology): “To prove the rst point, it suces to show that, if n is nite, then every multiplicative functional on CB(X) coincides with fk for some k. We use some ideas from [ 1 ].”
A lattice approach to narrow operators (2009, background): “Then, at least, one of the sets A = {t∈[0, 1] : y(t) = 1} or B = [0, 1]\A is of positive measure, say, μ(A) > 0.”
Context-theoretic Semantics for Natural Language: an Overview (2009, background): “…partial ordering associated with the lattice operations, deﬁned by Together with the l 1 norm, the vector lattice deﬁnes an Abstract Lebesgue space (Abramovich and Aliprantis, 2002) a vector space incorporating all the properties of a measure space, and thus can also be thought of as deﬁning a…”
Unbounded norm topology in Banach lattices (2016, background): “ipped with the norm kxke = inf λ>0 : |x| 6 λe is lattice isometric to C(K) for some compact Hausdorﬀ space K, with ecorresponding to the constant one function 1; see, e.g., Theorems 3.4 and 3.6 in [AA02]. If eis a strong unit in Xthen Ie = X; it is easy to see that in this case k·ke is equivalent”
Unbounded Order Convergence and Application to Martingales without Probability (2013, background): “respect to classical ﬁltrations is almost surely uo-Cauchy in F, where F is an order continuous Banach lattice with a weak unit (Corollary 5.7) . 2. Preliminaries 2.1. Some basic deﬁnitions. We adopt [1, 3, 20] as standard references for basic notions on Banach spaces, Banach lattices and vector lat”
On Order Convergence of Nets (2005, background): “For terminology and elementary properties of Riesz spaces not explained in this paper the reader can consult either of the following sources [ 1 ,2,7,8], or [11].”
A Context-Theoretic Framework for Compositionality in Distributional Semantics (2011, background): “Matrices can be viewed as operators on finite-dimensional vector spaces; in fact this lattice property extends to operators on certain infinite-dimensional spaces, the l p spaces, by the Riesz-Kantorovich theorem (Abramovich and Aliprantis 2002 ).”
Uo-convergence and its applications to Cesàro means in Banach lattices (2015, background): “We refer to [5, 4, 1] for unexplained terminology on vector and Banach lattices.”
COMPLETION OF CONE METRIC SPACES (2010, background): “For the infinite dimensional case the positive cones of AM − spaces can have non-empty interiors [2].”