46,311 research outputs found
Order continuous extensions of positive compact operators on Banach lattices
Let and be Banach lattices. Let be a vector sublattice of and
be an order continuous positive compact (resp. weakly
compact) operators. We show that if is an ideal or an order dense
sublattice of , then has a norm preserving compact (resp. weakly
compact) positive extension to which is likewise order continuous on .
In particular, we prove that every compact positive orthomorphism on an order
dense sublattice of extends uniquely to a compact positive orthomorphism on
.Comment: 7 page
On Transverse-Momentum Dependent Light-Cone Wave Functions of Light Mesons
Transverse-momentum dependent (TMD) light-cone wave functions of a light
meson are important ingredients in the TMD QCD factorization of exclusive
processes. This factorization allows one conveniently resum Sudakov logarithms
appearing in collinear factorization. The TMD light-cone wave functions are not
simply related to the standard light-cone wave functions in collinear
factorization by integrating them over the transverse momentum. We explore
relations between TMD light-cone wave functions and those in the collinear
factorization. Two factorized relations can be found. One is helpful for
constructing models for TMD light-cone wave functions, and the other can be
used for resummation. These relations will be useful to establish a link
between two types of factorization.Comment: add more discussions and reference
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