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Convergence of orthogonal series of projections in Banach spaces

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Jajte R., Paszkiewicz A.

Annales Polonici Mathematici

1997

tom 66

nr 1

137-153

For a sequence $(A_j)$ of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums $S_n = ∑^n_{j=1} A_j$ in a "strong" sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of $S_n$ (i.e. $S_{n}f → Af$ μ-a.e. for all f ∈ 𝓓(A)).

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Jajte R.

1 Paszkiewicz A.

1 1997

Wyniki wyszukiwania

Convergence of orthogonal series of projections in Banach spaces