103,247 research outputs found
Noncommutative Burkholder/Rosenthal inequalities II: applications
We show norm estimates for the sum of independent random variables in
noncommutative -spaces for following our previous work. These
estimates generalize the classical Rosenthal inequality in the commutative
case. Among applications, we derive an equivalence for the -norm of the
singular values of a random matrix with independent entries, and characterize
those symmetric subspaces and unitary ideals which can be realized as subspaces
of a noncommutative for .Comment: To appear in Isreal J; Mat
Regular subspaces of Dirichlet forms
The regular subspaces of a Dirichlet form are the regular Dirichlet forms
that inherit the original form but possess smaller domains. The two problems we
are concerned are: (1) the existence of regular subspaces of a fixed Dirichlet
form, (2) the characterization of the regular subspaces if exists. In this
paper, we will first research the structure of regular subspaces for a fixed
Dirichlet form. The main results indicate that the jumping and killing measures
of each regular subspace are just equal to that of the original Dirichlet form.
By using the independent coupling of Dirichlet forms and some celebrated
probabilistic transformations, we will study the existence and characterization
of the regular subspaces of local Dirichlet forms.Comment: This paper is collected in Festschrift Masatoshi Fukushima, In Honor
of Masatoshi Fukushima's Sanju, pp: 397-420, 201
The Geometry of Self-dual 2-forms
We show that self-dual 2-forms in 2n dimensional spaces determine a
dimensional manifold and the dimension of the maximal linear
subspaces of is equal to the (Radon-Hurwitz) number of linearly
independent vector fields on the sphere . We provide a direct proof
that for odd has only one-dimensional linear submanifolds.
We exhibit dimensional subspaces in dimensions which are multiples of
, for . In particular, we demonstrate that the seven dimensional
linear subspaces of also include among many other interesting
classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand,
Fairlie and Nuyts and a representation of
given by octonionic multiplication. We discuss the relation of the linear
subspaces with the representations of Clifford algebras.Comment: Latex, 15 page
Exact Markovian kinetic equation for a quantum Brownian oscillator
We derive an exact Markovian kinetic equation for an oscillator linearly
coupled to a heat bath, describing quantum Brownian motion. Our work is based
on the subdynamics formulation developed by Prigogine and collaborators. The
space of distribution functions is decomposed into independent subspaces that
remain invariant under Liouville dynamics. For integrable systems in
Poincar\'e's sense the invariant subspaces follow the dynamics of uncoupled,
renormalized particles. In contrast for non-integrable systems, the invariant
subspaces follow a dynamics with broken-time symmetry, involving generalized
functions. This result indicates that irreversibility and stochasticity are
exact properties of dynamics in generalized function spaces. We comment on the
relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.Comment: A few typos in the published version are correcte
Invariant subspaces of and preserving compatibility
Operators of multiplication by independent variables on the space of square
summable functions over the torus and its Hardy subspace are considered.
Invariant subspaces where the operators are compatible are described.Comment: 17 pages, 3 figure
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