scholarly journals Triangular matrix representation for selfadjoint operators in Krein spaces

1988 ◽  
Vol 14 (1) ◽  
pp. 165-202 ◽  
Author(s):  
Yoshiomi NAKAGAMI ◽  
Minoru TOMITA
Keyword(s):  
Matrix Representation ◽  
Triangular Matrix ◽  
Selfadjoint Operators ◽  
Krein Spaces

scholarly journals Normal generalized selfadjoint operators in Krein spaces

1998 ◽  
Vol 283 (1-3) ◽  
pp. 239-245 ◽  
Author(s):  
Scott A. McCullough ◽  
Leiba Rodman
Keyword(s):  
Selfadjoint Operators ◽  
Krein Spaces

scholarly journals Weyl type theorems for selfadjoint operators on Krein spaces

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6001-6016
Author(s):  
Il An ◽  
Jaeseong Heo
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Krein Space ◽  
Linear Operators ◽  
Fredholm Theory ◽  
Bounded Linear ◽  
Selfadjoint Operators ◽  
Krein Spaces ◽  
Weyl Type Theorems ◽  
Kreĭn Space

In this paper, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss when (a-)J-Weyl?s theorem or (a-)J-Browder?s theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.

Two-selfadjoint operators in Krein spaces

1996 ◽  
Vol 26 (2) ◽  
pp. 202-209 ◽  
Author(s):  
Scott A. McCullough ◽  
Leiba Rodman
Keyword(s):  
Selfadjoint Operators ◽  
Krein Spaces

TRIANGULAR MATRIX REPRESENTATION OF SKEW GENERALIZED POWER SERIES RINGS

2012 ◽  
Vol 05 (04) ◽  
pp. 1250027 ◽  
Author(s):  
Amit Bhooshan Singh
Keyword(s):  
Power Series ◽  
Matrix Representation ◽  
Triangular Matrix ◽  
Group Rings ◽  
Power Series Ring ◽  
Generalized Power Series ◽  
Series Ring ◽  
Skew Polynomial Rings ◽  
Monoid Homomorphism ◽  
Power Series Rings

Let R be a ring, (S, ≤) a strictly ordered monoid and ω : S → End (R) a monoid homomorphism. In this paper, we study the triangular matrix representation of skew generalized power series ring R[[S, ω]] which is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev–Neumann rings and generalized power series rings. We investigate that if R is S-compatible and (S, ω)-Armendariz, then the skew generalized power series ring has same triangulating dimension as R. Furthermore, if R is a PWP ring, then skew generalized power series is also PWP ring.

scholarly journals J-Self-Adjoint Projections in Krein Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Xiao-Ming Xu ◽  
Yile Zhao
Keyword(s):  
Matrix Representation ◽  
Krein Space ◽  
Operator Matrix ◽  
Matrix Representations ◽  
Isotropic Part ◽  
Fundamental Symmetry ◽  
Block Operator Matrix ◽  
Krein Spaces ◽  
Regular Subspace ◽  
Block Operator

Let ℋ be a Krein space with fundamental symmetry J. Starting with a canonical block-operator matrix representation of J, we study the regular subspaces of ℋ. We also present block-operator matrix representations of the J-self-adjoint projections for the regular subspaces of ℋ, as well as for the regular complements of the isotropic part in a pseudo-regular subspace of ℋ.

scholarly journals Algebras of right ample semigroups

2018 ◽  
Vol 16 (1) ◽  
pp. 842-861 ◽  
Author(s):  
Junying Guo ◽  
Xiaojiang Guo
Keyword(s):  
Inverse Semigroup ◽  
Matrix Representation ◽  
Triangular Matrix ◽  
Inverse Semigroups ◽  
Generalized Matrix ◽  
Upper Triangular Matrix

AbstractStrict RA semigroups are common generalizations of ample semigroups and inverse semigroups. The aim of this paper is to study algebras of strict RA semigroups. It is proved that any algebra of strict RA semigroups with finite idempotents has a generalized matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. In particular, it is proved that any algebra of finite right ample semigroups has a generalized upper triangular matrix representation whose degree is equal to the number of non-zero regular 𝓓-classes. As its application, we determine when an algebra of strict RA semigroups (right ample monoids) is semiprimitive. Moreover, we prove that an algebra of strict RA semigroups (right ample monoids) is left self-injective iff it is right self-injective, iff it is Frobenius, and iff the semigroup is a finite inverse semigroup.

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