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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
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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
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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
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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
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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
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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
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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
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Geometry of Fisher Information Metric and the Barycenter Map
Entropy, 2015 Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold \(X\).
Mitsuhiro Itoh, Hiroyasu Satoh
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On a locally compact monoid of cofinite partial isometries of ℕ with adjoined zero
Topological Algebra and its Applications, 2022 Let 𝒞ℕ be a monoid which is generated by the partial shift α : n↦n +1 of the set of positive integers ℕ and its inverse partial shift β : n + 1 ↦n. In this paper we prove that if S is a submonoid of the monoid Iℕ∞ of all partial cofinite isometries of ...
Gutik Oleg, Khylynskyi Pavlo
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Crossed Product of a C*-Algebra by a Semigroup of Interactions
Demonstratio Mathematica, 2014 The paper presents a construction of the crossed product of a C*-algebra by a commutative semigroup of bounded positive linear maps generated by partial isometries.
Kwaśniewski B. K.
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