Adjoint, Symmetric, and Self-adjoint Linear Operators

In the present work, using the concept of A -statistical convergence for double real sequences, we obtain a statistical approximation theorem for sequences of positive linear operators defined on the space of all real valued B -continuous functions on a compact subset of the real line. Furthermore, we display an application which shows that our new result is stronger than its classical version.

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On αβ-statistical convergence for sequences of fuzzy mappings and Korovkin type approximation theorem

Filomat ◽

10.2298/fil1712749k ◽

2017 ◽

Vol 31 (12) ◽

pp. 3749-3760 ◽

Cited By ~ 5

Author(s):

Ali Karaisa ◽

Uğur Kadak

Keyword(s):

Statistical Convergence ◽

Approximation Theorem ◽

Linear Operators ◽

Positive Linear Operators ◽

Bernstein Operator ◽

Korovkin Type Approximation Theorem ◽

Type Approximation ◽

Inclusion Relations ◽

Prior Investigation

Upon prior investigation on statistical convergence of fuzzy sequences, we study the notion of pointwise ??-statistical convergence of fuzzy mappings of order ?. Also, we establish the concept of strongly ??-summable sequences of fuzzy mappings and investigate some inclusion relations. Further, we get an analogue of Korovkin-type approximation theorem for fuzzy positive linear operators with respect to ??-statistical convergence. Lastly, we apply fuzzy Bernstein operator to construct an example in support of our result.

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Cline’s formula for g-Drazin inverses in a ring

Filomat ◽

10.2298/fil1908249c ◽

2019 ◽

Vol 33 (8) ◽

pp. 2249-2255

Author(s):

Huanyin Chen ◽

Marjan Abdolyousefi

Keyword(s):

Operator Theory ◽

Spectral Properties ◽

Associative Ring ◽

Linear Operators ◽

Drazin Inverse ◽

Bounded Linear Operators ◽

Bounded Linear ◽

Cline’S Formula

It is well known that for an associative ring R, if ab has g-Drazin inverse then ba has g-Drazin inverse. In this case, (ba)d = b((ab)d)2a. This formula is so-called Cline?s formula for g-Drazin inverse, which plays an elementary role in matrix and operator theory. In this paper, we generalize Cline?s formula to the wider case. In particular, as applications, we obtain new common spectral properties of bounded linear operators.

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Unbounded Linear Operators

10.1093/oso/9780198812050.003.0003 ◽

2018 ◽

Author(s):

D. E. Edmunds ◽

W. D. Evans

Keyword(s):

Hilbert Spaces ◽

Linear Operators ◽

Von Neumann ◽

Limit Circle ◽

Sectorial Operators ◽

Closed Operators ◽

The Stability ◽

Symmetric Operators ◽

Unbounded Linear Operators ◽

Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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Linear Operators in Banach Spaces

10.1093/oso/9780198812050.003.0001 ◽

2018 ◽

Author(s):

D. E. Edmunds ◽

W. D. Evans

Keyword(s):

Banach Spaces ◽

Linear Operators ◽

Fredholm Maps

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to derive important results later in the book.

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