Search results for "Subspace topology"
showing 10 items of 73 documents
Notes on the subspace perturbation problem for off-diagonal perturbations
2014
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear; arXiv:1310.4360 (2013)] is adapted. It is shown that, in contrast to the case of general perturbations, the corresponding optimization problem can not be reduced to a finite-dimensional problem. A suitable choice of the involved parameters provides an upper bound for the solution of the optimization problem. In particular, this yields a rotation bound on the subspaces that is stronger than the previously known one from [J. Reine Angew. Math. (2013), DOI:10.1515/cre…
A note on zeroes of real polynomials in $C(K)$ spaces
2008
For real C(K) spaces, we show that being injected in a Hilbert space is a 3-space property. As a consequence, we obtain that, when K does not carry a strictly positive Radon measure, every quadratic continuous homogeneous real-valued polynomial on C(K) admits a linear zero subspace enjoying a property which implies non-separability.
P-spaces and the Volterra property
2012
We study the relationship between generalizations of $P$-spaces and Volterra (weakly Volterra) spaces, that is, spaces where every two dense $G_\delta$ have dense (non-empty) intersection. In particular, we prove that every dense and every open, but not every closed subspace of an almost $P$-space is Volterra and that there are Tychonoff non-weakly Volterra weak $P$-spaces. These results should be compared with the fact that every $P$-space is hereditarily Volterra. As a byproduct we obtain an example of a hereditarily Volterra space and a hereditarily Baire space whose product is not weakly Volterra. We also show an example of a Hausdorff space which contains a non-weakly Volterra subspace…
Some representation theorems for sesquilinear forms
2016
The possibility of getting a Radon-Nikodym type theorem and a Lebesgue-like decomposition for a non necessarily positive sesquilinear $\Omega$ form defined on a vector space $\mathcal D$, with respect to a given positive form $\Theta$ defined on $\D$, is explored. The main result consists in showing that a sesquilinear form $\Omega$ is $\Theta$-regular, in the sense that it has a Radon-Nikodym type representation, if and only if it satisfies a sort Cauchy-Schwarz inequality whose right hand side is implemented by a positive sesquilinear form which is $\Theta$-absolutely continuous. In the particular case where $\Theta$ is an inner product in $\mathcal D$, this class of sesquilinear form cov…
A method for extracting subspace of deterministic sources from EEG data
2008
In this paper, an algorithm for separating linear subspaces of time-locked brain responses and other noise sources in multichannel electroencephalography data is proposed. The search criterion used by method discriminates time-locked brain components and noise components on the basis of the assumed deterministic behavior that the time-locked brain sources obey. The comprehensive derivation of the method is given together with the description and the analysis of the results of the method's application to simulated and real EEG data sets. The possibilities of improving the results are also discussed.
Diagrammatic approach to quantum search
2014
We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate perturbation theory's effects on them. Using this method, we give the first example of degenerate perturbation theory solving search on a graph whose evolution occurs in a subspace whose dimension grows with $N$.
Governing Survival Probability to Distill Quantum States
2005
A quantum system interacting with a repeatedly measured one undergoes a nonunitary time evolution pushing it into some specific subspaces. We deeply investigate the origin of the relevant selection rule, bringing to the light its connection with the survival probability related with the two-system interaction. The possibility of inducing an effective dynamics in the distilled subspace just during the distillation process is demonstrated.
DECENTRALIZED SUBSPACE PROJECTION IN LARGE NETWORKS
2018
A great number of applications in wireless sensor networks involve projecting a vector of observations onto a subspace dictated by prior information. Accomplishing such a task in a centralized fashion entails great power consumption, congestion at certain nodes, and suffers from robustness issues. A sensible alternative is to compute such projections in a decentralized fashion. To this end, recent works proposed schemes based on graph filters, which compute projections exactly with a finite number of local exchanges among sensor nodes. However, existing methods to obtain these filters are confined to reduced families of projection matrices or small networks. This paper proposes a method tha…
A characterization of the line set of an odd-dimensional Baer subspace
1990
Generalizing a theorem of Beutelspacher and Seeger, we consider line sets\(\mathcal{L}\) inP=PG(2t + 1,q),t ∈ IN, with the following properties: (1) any (t + 1)-dimensional subspace ofP contains at least one line of\(\mathcal{L}\), (2) if a pointx ofP is incident with at least two lines of\(\mathcal{L}\) then the points in the factor geometryP/x which are induced by the lines of\(\mathcal{L}\) throughx form a blocking set of type (t, 1) inP/x, (3) any line of\(\mathcal{L}\) is coplanar with at least one further line of\(\mathcal{L}\). We will show that the examples of minimal cardinality are exactly the line sets of Baer subspaces ofP.
Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection
2021
A large number of applications in decentralized signal processing includes projecting a vector of noisy observations onto a subspace dictated by prior information about the field being monitored. Accomplishing such a task in a centralized fashion in networks is prone to a number of issues such as large power consumption, congestion at certain nodes and suffers from robustness issues against possible node failures. Decentralized subspace projection is an alternative method to address those issues. Recently, it has been shown that graph filters (GFs) can be implemented to perform decentralized subspace projection. However, most of the existing methods have focused on designing GFs for symmetr…