Geodesic
On well-bounded operators of class Г
Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 1-5

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Let T be a linear operator acting in a Banach space X. It has been shown by Smart [5] and Ringrose [3] that, if X is reflexive, then T is well-bounded if and only if it may be expressed in the formwhere {E(λ)} is a suitable family of projections in X and the integral exists as the strong limit of Riemann sums. 
Jibril, Adnan A. S. On well-bounded operators of class Г. Glasgow mathematical journal, Tome 24 (1983) no. 1, pp. 1-5. doi: 10.1017/S0017089500004997
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[3] 3.Ringrose, J. R., On well-bounded operators. J. Austral. Math. Soc. 1 (1960), 334–343. Google Scholar

[4] 4.Ringrose, J. R., On well-bounded operators, II. Proc. London Math. Soc. (3) 13 (1963), 613–638. Google Scholar

[5] 5.Smart, D. R., Conditionally convergent spectral expansions. J. Austral. Math. Soc. 1 (1960) 319–333. Google Scholar

[6] 6.Turner, J. K., On well-bounded and decomposable operators. Proc. London Math. Soc. (3) 37 (1978), 521–544. Google Scholar

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