scholarly journals On the class of (A,n) - real power positive operators in semi-hilbertian space

2019 ◽  
Vol 25 (2) ◽  
pp. 161-166
Author(s):  
Abdelkader Benali
Keyword(s):  
Hilbert Space ◽  
Positive Integer ◽  
Positive Operator ◽  
Primary 47B20 ◽  
Positive Operators ◽  
Subject Classification ◽  
Inner Product ◽  
Space Operator ◽  
Real Power ◽  
Oblique Projections

In this paper, the concept of the class of n-Real power positive operators on a hilbert space defined by Abdelkader Benali in [1] is generalized when an additional semi-inner product is considered. This new concept is described by means of oblique projections. For a Hilbert space operator T ∈ B(H) is (A,n) - Real power positive operators for some positive operator A and for some positive integer n ifTn + T#n ≥A 0, n = 1,2,...Keywords: Real power, Semi-Hilbertian space, Semi-inner product, Positive operators. 2000Mathematics Subject Classification: Primary 47B20. Secondary 47B99

Every Invertible Hilbert Space Operator is a Product of Seven Positive Operators

1995 ◽  
Vol 38 (2) ◽  
pp. 230-236 ◽  
Author(s):  
N. Christopher Phillips
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Invertible Operator ◽  
Positive Operators ◽  
Space Operator ◽  
Von Neumann ◽  
Infinite Dimensional ◽  
Hilbert Space Operator

AbstractWe prove that every invertible operator in a properly infinite von Neumann algebra, in particular in L(H) for infinite dimensional H, is a product of 7 positive invertible operators. This improves a result of Wu, who proved that every invertible operator in L(H) is a product of 17 positive invertible operators.

Grüss-Landau inequalities for elementary operators and inner product type transformers in Q and Q* norm ideals of compact operators

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2447-2455
Author(s):  
Milan Lazarevic
Keyword(s):  
Hilbert Space ◽  
Probability Measure ◽  
Compact Operators ◽  
Product Type ◽  
Inner Product ◽  
Operator Inequality ◽  
Space Operator ◽  
Bounded Operators ◽  
Normal Operators ◽  
Elementary Operators

For a probability measure ? on ? and square integrable (Hilbert space) operator valued functions {A*t}t??, {Bt}t??, we prove Gr?ss-Landau type operator inequality for inner product type transformers |?? AtXBtd?(t)- ?? At d?(t)X ?? Btd?(t)|2? ? ||??AtA*td?(t)- |??A*td?(t)|2||? (?? B*tX*XBtd?(t)- |X?? Btd?(t)|2)?, for all X ? B(H) and for all ? ? [0,1]. Let p ? 2, ? to be a symmetrically norming (s.n.) function, ? (p) to be its p-modification, ? (p)* is a s.n. function adjoint to ?(p) and ||?||?(p)* to be a norm on its associated ideal C?(p)*(H) of compact operators. If X ? C?(p)*(H) and {?n}?n=1 is a sequence in (0,1], such that ??n=1 ?n = 1 and ??n=1 ||?n-1/2 An f||2+||?-1/2n B*nf||2 < +? for some families {An}? n=1 and {Bn}? n=1 of bounded operators on Hilbert space H and for all f ? H, then ||?? n=1 ?-1n AnXBn-?? n=1 AnX ?? n=1 Bn||?(p)* ? ||???n=1 ?-1n |An|2-|??n=1 An|2 X ? ??n=1 ?-1n |B*n|2-|??n=1 B*n|2||?(p)+, if at least one of those operator families consists of mutually commuting normal operators. The related Gr?ss-Landau type ||?||?(p) norm inequalities for inner product type transformers are also provided.

A Class of Polynomials in Self-Adjoint Operators in Spaces with an Indefinite Metric

1968 ◽  
Vol 20 ◽  
pp. 673-678 ◽  
Author(s):  
C.-Y. Lo
Keyword(s):  
Hilbert Space ◽  
Positive Integer ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
Indefinite Metric ◽  
Indefinite Inner Product ◽  
Image Position ◽  
Fixed Positive Integer ◽  
Adjoint Operators ◽  
Usual Product

Let H be a Hilbert space with the usual product [x, y] and with an indefinite inner product (x, y) which, for some orthogonal decompositionin H, is defined bywhereand dim H1 = κ, a fixed positive integer.

A mass-conserved tumor invasion system with quasi-variational degenerate diffusion

2021 ◽  
pp. 1-66
Author(s):  
Akio Ito
Keyword(s):  
Hilbert Space ◽  
Tumor Cells ◽  
Tumor Invasion ◽  
Real Hilbert Space ◽  
Initial Boundary ◽  
Inner Product ◽  
Boundary Problems ◽  
Theory Of Evolution ◽  
Cross Diffusion ◽  
Variational Structure

This paper deals with a nonlinear system (S) composed of three PDEs and one ODE below: [Formula: see text] The system (S) was proposed as one of the mathematical models which describe tumor invasion phenomena with chemotaxis effects. The most important and interesting point is that the diffusion coefficient of tumor cells, denoted by [Formula: see text], is influenced by both nonlocal effect of a chemical attractive substance, denoted by [Formula: see text], and the local one of extracellular matrix, denoted by [Formula: see text]. From this point, the first PDE in (S) contains a nonlinear cross diffusion. Actually, this mathematical setting gives an inner product of a suitable real Hilbert space, which governs the dynamics of the density of tumor cells [Formula: see text], a quasi-variational structure. Hence, the first purpose in this paper is to make it clear what this real Hilbert space is. After this, we show the existence of strong time local solutions to the initial-boundary problems associated with (S) when the space dimension is [Formula: see text] by applying the general theory of evolution inclusions on real Hilbert spaces with quasi-variational structures. Moreover, for the case [Formula: see text] we succeed in constructing a strong time global solution.

scholarly journals About the construction of fuzzy inner product

2006 ◽  
Vol 3 (3) ◽  
pp. 456-464
Author(s):  
Baghdad Science Journal
Keyword(s):  
Positive Integer ◽  
Inner Product

In this research for each positive integer integer and is accompanied by connecting that number with the number of Bashz Attabq result any two functions midwives to derive a positive integer so that there is a point

scholarly journals Approximation of positive operators by analytic vectors

2020 ◽  
Vol 12 (2) ◽  
pp. 412-418
Author(s):  
M.I. Dmytryshyn
Keyword(s):  
Banach Space ◽  
Positive Operator ◽  
Invariant Subspaces ◽  
Positive Operators ◽  
Interpolation Spaces ◽  
Jackson Type ◽  
Normalization Factor ◽  
Approximation Spaces ◽  
Similar Role ◽  
Approximation Errors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

A subclass of meromorphic functions defined by a certain integral operator on Hilbert space

2017 ◽  
Vol 26 (2) ◽  
pp. 115-124
Author(s):  
Arzu Akgül
Keyword(s):  
Hilbert Space ◽  
Integral Operator ◽  
Meromorphic Functions ◽  
Hadamard Product ◽  
Extreme Points ◽  
Space Operator ◽  
Integral Means ◽  
New Class ◽  
Coefficient Inequality ◽  
Hilbert Space Operator

In the present paper, we introduce and investigate a new class of meromorphic functions associated with an integral operator, by using Hilbert space operator. For this class, we obtain coefficient inequality, extreme points, radius of close-to-convex, starlikeness and convexity, Hadamard product and integral means inequality.

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