Rademacher series in Hilbert space

1987 ◽  
Vol 36 (4) ◽  
pp. 535-540
Author(s):  
A. A. Ryabinin
Keyword(s):  
Hilbert Space ◽  
Rademacher Series

scholarly journals An operator ideal generated by Orlicz spaces

2019 ◽  
Vol 376 (3-4) ◽  
pp. 1675-1703
Author(s):  
Mieczysław Mastyło
Keyword(s):  
Hilbert Space ◽  
Wide Class ◽  
Orlicz Spaces ◽  
Asymptotic Estimates ◽  
Approximation Numbers ◽  
Diagonal Operators ◽  
Finite Dimensional ◽  
Rademacher Series ◽  
Vector Valued ◽  
Banach Sequence

Abstract Absolutely $$\varphi $$φ-summing operators between Banach spaces generated by Orlicz spaces are investigated. A variant of Pietsch’s domination theorem is proved for these operators and applied to prove vector-valued inequalities. These results are used to prove asymptotic estimates of $$\pi _\varphi $$πφ-summing norms of finite-dimensional operators and also diagonal operators between Banach sequence lattices for a wide class of Orlicz spaces based on exponential convex functions $$\varphi $$φ. The key here is the description of a space of coefficients of the Rademacher series in this class of Orlicz spaces, proved via interpolation methods. As by-product, some absolutely $$\varphi $$φ-summing operators on the Hilbert space $$\ell _2$$ℓ2 are characterized in terms of its approximation numbers.

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space

On Definition of Expansion Probabilistic Hilbert Space

2018 ◽  
Vol 14 (3) ◽  
pp. 59-73
Author(s):  
Ahmed Hasan Hamed ◽  
Keyword(s):  
Hilbert Space ◽  
Definition Of

ON A GENERALIZATION OF THE HILBERT SPACE

1989 ◽  
Vol 22 (1) ◽  
pp. 1-20
Author(s):  
Hubert Wywcki
Keyword(s):  
Hilbert Space

The Essence of Quantum Computing

2018 ◽  
Author(s):  
Rajendra K. Bera
Keyword(s):  
Hilbert Space ◽  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Turing Machines ◽  
Classical Physics ◽  
Core Set ◽  
The World ◽  
Subordinate Role

It now appears that quantum computers are poised to enter the world of computing and establish its dominance, especially, in the cloud. Turing machines (classical computers) tied to the laws of classical physics will not vanish from our lives but begin to play a subordinate role to quantum computers tied to the enigmatic laws of quantum physics that deal with such non-intuitive phenomena as superposition, entanglement, collapse of the wave function, and teleportation, all occurring in Hilbert space. The aim of this 3-part paper is to introduce the readers to a core set of quantum algorithms based on the postulates of quantum mechanics, and reveal the amazing power of quantum computing.

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