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Mention H. Amann's 'Linear and Quasilinear Parabolic Problems' vol. 2
anonymous
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  • S. Gel'fand, Yu. Manin, Methods of homological algebra, first appeared in Russian as Методы гомологической алгебры. Введение в теорию когомологий и производные категории. Т. 1 (that is VOLUME 1). Volume 2 has been given up and the Springer Western edition does not cite Russian original, has many typing errors in formulas which Russian original does not have and it scraped off the tome 1 from the title.

  • M. Demazure, P. Gabriel, Groupes algebriques, tome 1, Mason and Cie, Paris 1970 -- later volumes never appeared

  • Z. Semadeni, Banach Spaces of Continuous Functions, Polish Scientific Publishers, Warzawa, 1971, never appeared from the Polish Sci. Publ. There is however a different book with a similar title in Springer in 1982, Schauder bases in Banach spaces of continuous functions. Lecture Notes in Mathematics 918. Springer 1982. v+136 pp. MR83g:46023.

  • John W. Gray, Formal category theory: adjointness for 2-categories, Lecture Notes in Mathematics 391, Springer-Verlag 1974. xii+282 pp. has been envisioned as a m3 volume project on formal category theory, some material is mentioned in volume 1 and never appeared. The monograph is very innovative and some of the material from the latter volumes was undoubtfully sketched by the author in some detail. The author later drifted to theoretical computer science.

  • John Duskin started a paper in several parts "Nerves of bicategories", part I appeared with great delay, partly due serious health problem the author experienced few years ago. Second and third part did not appear, although the contents description looks very promising. We wish the author good health and more to be seen!

  • H. Amann, Linear and Quasilinear Parabolic Problems, Volume II: Function Spaces and Linear Differential Operators, 1999. His article Compact embeddings of vector-valued Sobolev and Besov spaces (which ended up appearing only in 2000, thus after the book was supposed to come out) refers repeatedly to this book for details and extensions, even referencing certain sections by number. As of 2017, it appears the book still has not appeared. The structure has changed at least to some extent, too, so that what was meant to be the first chapter will no longer be included (it is made available for free from http://user.math.uzh.ch/amann/books.html instead).

Grothendieck planned not only later EGAs but also later SGA (e.g. some Berthelot's works in SGA 8). Bourbaki Elements are of course never finished as well (an now are very slow, asymptotically stalling) as the German encyclopedic work by Klein's students at the beginning of the 20th century. M. M. Postnikov wrote two volumes of a course on algebraic topology in Russian about basics of homotopy theory and promised the homology in "next semester" but no books appeared on that.

Zoran Skoda
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