13.4. Factorization of operator functions (classification of holomorphic Hilbert space bundles over the Riemannian sphere)

1984 ◽  
Vol 26 (5) ◽  
pp. 2164-2166
Author(s):  
J. Leiterer
Keyword(s):  
Hilbert Space ◽  
Operator Functions ◽  
Riemannian Sphere

scholarly journals Global anomalies on the Hilbert space

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Diego Delmastro ◽  
Davide Gaiotto ◽  
Jaume Gomis
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Symmetry Algebra ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Strongly Coupled ◽  
Topological Quantum ◽  
Anomalous Theory

Abstract We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology “layers” that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2 + 1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.

scholarly journals Correct solvability and representation of the solutions of Volterra integro-differential equations with exponential-fractional kernels

2019 ◽  
Vol 488 (5) ◽  
pp. 476-480
Author(s):  
V. V. Vlasov ◽  
N. A. Rautian
Keyword(s):  
Hilbert Space ◽  
Spectral Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Unbounded Operator ◽  
Strong Solutions ◽  
Abstract Form ◽  
Partial Differential ◽  
Operator Functions ◽  
Well Posed

For abstract integro-differential equations with unbounded operator coefficients in a Hilbert space, we study the well-posed solvability of initial problems and carry out spectral analysis of the operator functions that are symbols of these equations. This allows us to represent the strong solutions of these equations as series in exponentials corresponding to points of the spectrum of operator functions. The equations under study are the abstract form of linear integro-partial differential equations arising in viscoelasticity and several other important applications.

Analysis and Classification of MoCap Data by Hilbert Space Embedding-Based Distance and Multikernel Learning

2019 ◽  
pp. 186-193
Author(s):  
Juan Diego Pulgarin-Giraldo ◽  
Andres Marino Alvarez-Meza ◽  
Steven Van Vaerenbergh ◽  
Ignacio Santamaría ◽  
German Castellanos-Dominguez
Keyword(s):  
Hilbert Space

The Classification of Factors is not Smooth

1973 ◽  
Vol 25 (1) ◽  
pp. 96-102 ◽  
Author(s):  
E. J. Woods
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Explicit Construction ◽  
Countable Family ◽  
Borel Sets ◽  
Isomorphism Classes ◽  
Borel Structure

There is a natural Borel structure on the set F of all factors on a separable Hilbert space [3]. Let denote the algebraic isomorphism classes in F together with the quotient Borel structure. Now that various non-denumerable families of mutually non-isomorphic factors are known to exist [1; 6; 8; 10; 11; 12; 13], the most obvious question to be resolved is whether or not is smooth (i.e. is there a countable family of Borel sets which separate points). We answer this question negatively by an explicit construction.

scholarly journals Spectral classification of operators and operator functions

1976 ◽  
Vol 82 (4) ◽  
pp. 587-590 ◽  
Author(s):  
I. Gohberg ◽  
M. A. Kaashoek ◽  
D. C. Lay
Keyword(s):  
Spectral Classification ◽  
Operator Functions

Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators

2010 ◽  
Vol 62 (2) ◽  
pp. 305-319
Author(s):  
He Hua ◽  
Dong Yunbai ◽  
Guo Xianzhou
Keyword(s):  
Hilbert Space ◽  
Jacobson Radical ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Bounded Linear ◽  
Similarity Classification ◽  
Strongly Irreducible ◽  
Decomposable Operators ◽  
Decomposable Operator

AbstractLet 𝓗 be a complex separable Hilbert space and ℒ(𝓗) denote the collection of bounded linear operators on 𝓗. In this paper, we show that for any operator A ∈ ℒ(𝓗), there exists a stably finitely (SI) decomposable operator A∈, such that ‖A−A∈‖ 𝓗 ∈ andA′(A∈)/ rad A′(A∈) is commutative, where rad A′(A∈) is the Jacobson radical of A′(A∈). Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen–Douglas operators given by C. L. Jiang.

scholarly journals Yang-Baxter and the Boost: splitting the difference

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Paul Ryan
Keyword(s):  
Hilbert Space ◽  
Sigma Model ◽  
Spin Chains ◽  
Baxter Equation ◽  
Regular Solutions ◽  
One Dimensional ◽  
Difference Form ◽  
The Difference ◽  
The One

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

scholarly journals Resolvents of functions of operators with Hilbert-Schmidt hermitian components

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 4937-4947
Author(s):  
Michael Gil’
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Convex Hull ◽  
Operator Function ◽  
Separable Hilbert Space ◽  
Operator Equations ◽  
Bounded Linear ◽  
Operator Functions ◽  
Schmidt Operator ◽  
Unit Operator

Let H be a separable Hilbert space with the unit operator I. We derive a sharp norm estimate for the operator function (?I-f(A))-1 (? ? C), where A is a bounded linear operator in H whose Hermitian component (A- A*)/2i is a Hilbert-Schmidt operator and f(z) is a function holomorphic on the convex hull of the spectrum of A. Here A* is the operator adjoint to A. Applications of the obtained estimate to perturbations of operator equations, whose coefficients are operator functions and localization of spectra are also discussed.

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