Abstract
In this monograph, we mainly handle real Banach spaces and Hilbert spaces and real linear operators. For this reason, Banach spaces, Hilbert spaces and linear operators always mean real ones if they are not otherwise specified. However, they are all obtained as a real part (in a certain sense) of some complex Banach spaces, Hilbert spaces or complex linear operators. This means that we can fortunately utilize the powerful tools developed in Complex Functional Analysis. The first half of this chapter is devoted to reviewing the most convenient way to utilize the tools of Complex Functional Analysis to real spaces and operators. These results were originally presented in the paper (Yagi (Bull South Ural State Univ Ser MMCS 10:97–112, 2017)).
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Yagi, A. (2021). Preliminaries. In: Abstract Parabolic Evolution Equations and Łojasiewicz–Simon Inequality I. SpringerBriefs in Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-1896-3_1
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DOI: https://doi.org/10.1007/978-981-16-1896-3_1
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