9,095 research outputs found
Frames and bases in tensor products of Hilbert spaces and Hilbert C*-modules
In this article, we study tensor product of Hilbert -modules and Hilbert
spaces. We show that if is a Hilbert -module and is a Hilbert
-module, then tensor product of frames (orthonormal bases) for and
produce frames (orthonormal bases) for Hilbert -module , and we get more results.
For Hilbert spaces and , we study tensor product of frames of
subspaces for and , tensor product of resolutions of the identities of
and , and tensor product of frame representations for and .Comment: 12 page
Serre's Tensor Construction and Moduli of Abelian Schemes
Given a polarized abelian scheme with action by a ring, and a projective
finitely presented module over that ring, Serre's tensor construction produces
a new abelian scheme. We show that to equip these abelian schemes with
polarizations it's enough to equip the projective modules with non-degenerate
positive-definite hermitian forms. As an application, we relate certain moduli
spaces of principally polarized abelian schemes with action by the ring of
integers of a CM field. More specifically, we consider integral models of
zero-dimensional Shimura varieties associated to compact unitary groups. We
show that all abelian schemes in such moduli spaces are, \'etale locally over
their base schemes, Serre constructions of CM abelian schemes with
positive-definite hermitian modules. We also describe the morphisms between
such objects in terms of morphisms between the constituent data, and formulate
these relations as an isomorphism of algebraic stacks.Comment: 36 page
Internet and Users. Who is the Reader?
Internet has turned into a fundamental component of everyday life, as it plays a major role in
advancing the globalization process. Globalization was fostered by the idea of creating equalaccess
opportunities for all and facilitating communication worldwide. Using internet as the core
platform, billions of people try to access and benefit from this opportunity through search
engines, service providers, websites and social media. However, given the profound difference
between internet and user’s languages, users end up on relying on search engines and tools to
translate their ideas into a computer-readable language and derive information from them.
In order to provide the best possible services, search engines and social media need to
accumulate comprehensive data on each user’s identity. The challenge is that once they are fed
with convenient information on each user, they tend to personalize the idea they grasp of him or
her based on their given regulations and policies, which in the mid- and long-term results in
managing users’ access to information..
By applying the reader-response theory, this paper seeks to focus on the challenges stemming
from the adoption of users’ personalized profiles by Google, Facebook and Amazon as the most
common part of users’ performance in internet. It also explores how the reading differences of
the users and the tools result not only in personalized versions of users, but also engender an
unrecognized virtual in-betweenness of users’ own perception of themselves and the tools’
perception of users
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