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Locating the range of an operator on a Hilbert space
 Bull. London Math. Soc
, 1992
"... In classical operator theory it is taken for granted that we can project onto the closure of the range of an operator T on a Hilbert space H. In a constructive development of operator theory, to which this note is a contribution, this projection exists if and only if ran(r), the range of T, is locat ..."
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In classical operator theory it is taken for granted that we can project onto the closure of the range of an operator T on a Hilbert space H. In a constructive development of operator theory, to which this note is a contribution, this projection exists if and only if ran(r), the range of T, is located, in the sense that the distance
Adjoints, absolute values and polar decompositions
 Journal of Operator Theory
"... Abstract. Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the existence of an adjoint, and a general notion of a polar decomposition is developed. The Rie ..."
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Abstract. Various questions about adjoints, absolute values and polar decompositions of operators are addressed from a constructive point of view. The focus is on bilinear forms. Conditions are given for the existence of an adjoint, and a general notion of a polar decomposition is developed. The Riesz representation theorem is proved without countable choice.