We construct a hereditarily indecomposable Banach space with dual space isomorphic to$ℓ$_{1}. Every bounded linear operator on this space is expressible as λ$I$+$K$, with λ a scalar and$K$compact.
Brown G, Moran W. Bernoulli measure algebras[J]. Acta Mathematica, 1974, 132(1): 77-109.
2
Bohnstengel J, Jorgensen P E. Geometry of spectral pairs[C]., 2011, 1(1): 69-99.
3
Sasane A. An abstract Nyquist criterion containing old and new results[J]. Journal of Mathematical Analysis and Applications, 2010, 370(2): 703-715.
4
E A Gorin. Fragments of the research biography of D.A.?Raikov: harmonic analysis. 2006.
5
Taylor J L. On the spectrum of a measure[J]. Advances in Mathematics, 1974, 12(4): 451-463.
6
Stephen T L Choy. Hewitt-Zuckerman Semigroups in the Structure Semigroups of Measure Algebras. 1977.
7
J W Baker. Invariant convolution algebras. 1973.
8
Евгений Алексеевич Горин · Evgenii Alekseevich Gorin. Фрагменты научной биографии Д. А. Райкова: гармонический анализ@@@Fragments of the research biography of D. A. Raikov: harmonic anal…. 2006.