Results 1 to 10 of about 1,012 (145)
Adversarial Robustness with Partial Isometry [PDF]
EntropyDespite their remarkable performance, deep learning models still lack robustness guarantees, particularly in the presence of adversarial examples. This significant vulnerability raises concerns about their trustworthiness and hinders their deployment in ...
Loïc Shi-Garrier +2 more
doaj +5 more sources
Extending partial isometries [PDF]
Israel Journal of Mathematics, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sławomir Solecki
exaly +3 more sources
On the decomposition of families of quasinormal operators [PDF]
Opuscula Mathematica, 2013 The canonical injective decomposition of a jointly quasinormal family of operators is given. Relations between the decomposition of a quasinormal operator T and the decomposition of a partial isometry in the polar decomposition of T are described.
Zbigniew Burdak
doaj +1 more source
Semigroups of partial isometries [PDF]
Semigroup Forum, 2013 We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of self-adjoint semigroups of partial isometries. We obtain a general structure result showing that every self-adjoint semigroup
Popov AI, Radjavi H
openaire +4 more sources
On partial isometries with circular numerical range
Concrete Operators, 2021 In their LAMA 2016 paper Gau, Wang and Wu conjectured that a partial isometry A acting on ℂn cannot have a circular numerical range with a non-zero center, and proved this conjecture for n ≤ 4. We prove it for operators with rank A = n − 1 and any n.
Wegert Elias, Spitkovsky Ilya
doaj +1 more source
On unitary equivalence of bilateral operator valued weighted shifts [PDF]
Opuscula Mathematica, 2019 We establish a characterization of unitary equivalence of two bilateral operator valued weighted shifts with quasi-invertible weights by an operator of diagonal form.
Jakub Kośmider
doaj +1 more source
AdS3/AdS2 degression of massless particles
Journal of High Energy Physics, 2021 We study a 3d/2d dimensional degression which is a Kaluza-Klein type mechanism in AdS3 space foliated into AdS2 hypersurfaces. It is shown that an AdS3 massless particle of spin s = 1, 2, …, ∞ degresses into a couple of AdS2 particles of equal energies E
Konstantin Alkalaev, Alexander Yan
doaj +1 more source
Factorization of matrices into partial isometries [PDF]
Proceedings of the American Mathematical Society, 1989 In this paper, we characterize complex square matrices which are expressible as products of partial isometries and orthogonal projections. More precisely, we show that a matrix T T
Kuo, Kunghwang, Wu, Peiyuan
openaire +2 more sources
On families of twisted power partial isometries
Karpatsʹkì Matematičnì Publìkacìï, 2022 We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\lambda_{ij}\in\mathbb C$, $|\lambda_{ij}|=1$.
V.L. Ostrovskyi +2 more
doaj +1 more source
Endomorphisms of the Toeplitz algebra
Учёные записки Казанского университета: Серия Физико-математические науки, 2023 This article describes all injective endomorphisms of the classical Toeplitz algebra. Their connection with endomorphisms of the algebra of continuous functions on the unit circle and with coverings over the unit circle was considered.
S. A. Grigoryan, A. Yu. Kuznetsova
doaj +1 more source