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Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1972) P. Enflo's example of a separable space without approximation property and thus without Schauder basis.

3. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

4. (1974) B. Tsirelson's space without $c_0$ and $\ell_p$.

5. (1975) P. Enflo's example of an operator without non-trivial invariant subspaces.

6. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

7. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).

Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1972) P. Enflo's example of a separable space without approximation property and thus without Schauder basis.

3. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

4. (1974) B. Tsirelson's space without $c_0$ and $\ell_p$.

5. (1975) P. Enflo's example of an operator without non-trivial invariant subspaces.

6. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

7. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).

Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

3. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

4. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).

Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1972) P. Enflo's example of a separable space without approximation property and thus without Schauder basis.

3. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

4. (1974) B. Tsirelson's space without $c_0$ and $\ell_p$.

5. (1975) P. Enflo's example of an operator without non-trivial invariant subspaces.

6. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

7. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).

Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

3. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

4. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).

I'm not convinces these all meet the criterion of being unexpected. In the case of (4), people expected a construction was possible, but for a long time nothing seemed to work and some very bright people had worked on the problem.

Listing examples is easy in Banach space theory.

1. (1950) R.C.James' construction of non-reflexive (Banach) space isometric to its bidual.

2. (1974) R.C.James' construction of a space whose dual is non-separable and all of its subspaces contain a copy of $\ell_2$.

3. (1993) Gowers and Maurey's construction of a space such that no infinite dimensional subspace has a non-trivial complemented subspace (hereditarily indecomposable).

4. (2010) Argyros and Haydon's construction of a space on which every operator is a scalar multiple of the identity plus a compact operator (see Gowers' blog).