scholarly journals Addendum/erratum: ``Partial {$\sp \ast$}-algebras of closed linear operators in Hilbert space'' [Publ. Res. Inst. Math. Sci. { 21 } (1985), no. 1, 205--236; MR0780895 (86g:47057)]

1986 ◽  
Vol 22 (3) ◽  
pp. 507-511 ◽  
Author(s):  
J.-P. Antoine ◽  
W. Karwowski
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Closed Linear Operators

A Note on the Adjoint of the Product of Operators

1970 ◽  
Vol 13 (1) ◽  
pp. 39-45
Author(s):  
Chia-Shiang Lin
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Closed Subspace ◽  
Linear Operators ◽  
Finite Codimension ◽  
Restricted Condition ◽  
Closed Linear Operators

Cordes and Labrousse ([2] p. 697), and Kaniel and Schechter ([6] p. 429) showed that if S and T are domain-dense closed linear operators on a Hilbert space H into itself, the range of S is closed in H and the codimension of the range of S is finite, then, (TS)* = S*T*. With a somewhat different approach and more restricted condition on S, the same assertion was obtained by Holland [5] recently, that S is a bounded everywhere-defined linear operator whose range is a closed subspace of finite codimension in H.

scholarly journals Is it possible to give a more precise formulation of the criterion of maximal accretivity for one extension of nonnegative operator?

2020 ◽  
Vol 54 (1) ◽  
pp. 107-108
Author(s):  
O. G. Storozh
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Precise Formulation ◽  
Nonnegative Operator ◽  
Convenient Form ◽  
Necessary And Sufficient ◽  
Closed Linear Operators

The conditions being necessary and sufficient for maximal accretivity and maximal nonnegativity of some closed linear operators in Hilbert space are announced. The following problem is proposed: write down these conditions in more convenient form (one of the admissible variants is indicated).

scholarly journals Closed linear operators with domain containing their range

1984 ◽  
Vol 27 (2) ◽  
pp. 229-233 ◽  
Author(s):  
Schôichi Ôta
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Linear Operator ◽  
Linear Operators ◽  
Closed Linear Operator ◽  
Unbounded Operators ◽  
Densely Defined ◽  
Closed Linear Operators

In connection with algebras of unbounded operators, Lassner showed in [4] that, if T is a densely defined, closed linear operator in a Hilbert space such that its domain is contained in the domain of its adjoint T* and is globally invariant under T and T*,then T is bounded. In the case of a Banach space (in particular, a C*-algebra) weshowed in [6] that a densely defined closed derivation in a C*-algebra with domaincontaining its range is automatically bounded (see the references in [6] and [7] for thetheory of derivations in C*-algebras).

scholarly journals On a question of A. E. Nussbaum on measurability of families of closed linear operators in a Hilbert space

2011 ◽  
Vol 188 (1) ◽  
pp. 195-219 ◽  
Author(s):  
Fritz Gesztesy ◽  
Alexander Gomilko ◽  
Fedor Sukochev ◽  
Yuri Tomilov
Keyword(s):  
Hilbert Space ◽  
Linear Operators ◽  
Closed Linear Operators

A general version of Neubauer’s lemma and closed range almost closed operators

2019 ◽  
Vol 13 (07) ◽  
pp. 2050124
Author(s):  
Abdellah Gherbi ◽  
Sanaa Messirdi ◽  
Bekkai Messirdi
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Closed Operator ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
General Version ◽  
Closed Range ◽  
Closed Operators ◽  
Necessary And Sufficient ◽  
Closed Linear Operators

In this paper, almost closed subspaces and almost closed linear operators are described in a Hilbert space. We show Neubauer’s lemma and we give necessary and sufficient conditions for an almost closed operator to be with closed range and we exhibit sufficient conditions under which it is either closed or closable.

Some properties of D-weak operator topology

2020 ◽  
Vol 70 (3) ◽  
pp. 753-758
Author(s):  
Marcel Polakovič
Keyword(s):  
Hilbert Space ◽  
Effect Algebra ◽  
Linear Subspace ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weak Operator Topology ◽  
Generalized Effect Algebra ◽  
Weak Operator ◽  
Dense Linear Subspace

AbstractLet 𝓖D(𝓗) denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace D of a Hilbert space 𝓗. The D-weak operator topology (introduced by other authors) on 𝓖D(𝓗) is investigated. The corresponding closure of the set of bounded elements of 𝓖D(𝓗) is the whole 𝓖D(𝓗). The closure of the set of all unbounded elements of 𝓖D(𝓗) is also the set 𝓖D(𝓗). If Q is arbitrary unbounded element of 𝓖D(𝓗), it determines an interval in 𝓖D(𝓗), consisting of all operators between 0 and Q (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the D-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

scholarly journals Duality and the existence of weakly completely continuous elements in aB*-algebra

1972 ◽  
Vol 13 (1) ◽  
pp. 56-60 ◽  
Author(s):  
B. J. Tomiuk
Keyword(s):  
Hilbert Space ◽  
Left Ideal ◽  
Linear Operators ◽  
Completely Continuous ◽  
Identity Modulo

Ogasawara and Yoshinaga [9] have shown that aB*-algebra is weakly completely continuous (w.c.c.) if and only if it is*-isomorphic to theB*(∞)-sum of algebrasLC(HX), where eachLC(HX)is the algebra of all compact linear operators on the Hilbert spaceHx.As Kaplansky [5] has shown that aB*-algebra isB*-isomorphic to theB*(∞)-sum of algebrasLC(HX)if and only if it is dual, it follows that a5*-algebraAis w.c.c. if and only if it is dual. We have observed that, if only certain key elements of aB*-algebraAare w.c.c, thenAis already dual. This observation constitutes our main theorem which goes as follows.A B*-algebraAis dual if and only if for every maximal modular left idealMthere exists aright identity modulo M that isw.c.c.

Spectral value sets of closed linear operators

2000 ◽  
Vol 456 (1998) ◽  
pp. 1397-1418 ◽  
Author(s):  
E. Gallestey ◽  
D. Hinrichsen ◽  
A. J. Pritchard
Keyword(s):  
Linear Operators ◽  
Value Sets ◽  
Closed Linear Operators
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