Sentence examples for deficiency spaces from inspiring English sources

Such a family is obtained by giving a Kreın-like formula where the role of the deficiency spaces is played by the dual pair (X, X′); the parameter Θ belongs to the space of symmetric operators from X′ to X.

Since (mathcal{A}) is a symmetric densely defined operator, then it is sufficient to show that the deficiency spaces are the null spaces and hence (mathcal{A}=mathcal{A}^).

It describes a one-to-one correspondence between these derivations and pairs S,L, where S are symmetric densely operators on H and L are J-orthogonal π-reflexive lattices of subspaces in the deficiency spaces of S. The domains D of these *-derivations are associated with some non-selfadjoint reflexive algebras Aδ of bounded operators on H⊕H.

The domains of ( A − i I ) − 1 and ( A + i I ) − 1 are exactly H. Consequently, the ranges of ( A − i I ) and ( A + i I ) are also H. Hence the deficiency spaces of A are N − i : = N ( A ∗ + i I ) = R ( A − i I ) ⊥ = H 1 ⊥ = { 0 }, N i : = N ( A ∗ − i I ) = R ( A + i I ) ⊥ = H 1 ⊥ = { 0 }.

Through flow cytometric assays and molecular biology analyses, this diagnostic system will improve medical surveillance of astronauts and will be used to test countermeasures aimed at preventing immune deficiency during space missions.

Lush but confined, the mountains are a cushy prison, a Hotel California for apex predators, whose future is threatened by a double deficiency: not enough space for a group of lions with not enough genetic differences among them.

Several respondents stated that while reorganization of clinic space had freed up some rooms by reducing duty-station duplication (e.g. a single pharmacy dispensary vs separate ART and OPD dispensaries), it did not ultimately address overall space deficiency.

Therefore, the most important methods of investigation for this subgroup are: MRI and radiographs to evaluate e.g. AC-osteoarthritis and subacromial osteophytes, impingement on the superior aspect of the glenoid, impingement at the outlet of the shoulder, coracoid impingement, and other (subacromial) pathologies or impinging structures causing a deficiency of subacromial space.

For a symmetric operator or relation A with infinite deficiency indices in a Hilbert space we develop an abstract framework for the description of symmetric and self-adjoint extensions AΘ of A as restrictions of an operator or relation T which is a core of the adjoint A∗.

The Parks Department has finally begun to address the deficiencies of its play spaces.

The study also highlighted a number of serious deficiencies in certain green spaces, which will need to be addressed in future action plans and replanning projects as an essential step in ensuring that they meet the real needs and expectations of the target population.