diff --git a/Project.toml b/Project.toml
index 98cdb44..c351587 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "InfiniteLinearAlgebra"
 uuid = "cde9dba0-b1de-11e9-2c62-0bab9446c55c"
-version = "0.6.9"
+version = "0.6.10"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"
diff --git a/src/InfiniteLinearAlgebra.jl b/src/InfiniteLinearAlgebra.jl
index 61a3e8e..b3eb2ef 100644
--- a/src/InfiniteLinearAlgebra.jl
+++ b/src/InfiniteLinearAlgebra.jl
@@ -28,7 +28,8 @@ import BlockArrays: AbstractBlockVecOrMat, sizes_from_blocks, _length, BlockedUn
 
 import BandedMatrices: BandedMatrix, bandwidths, AbstractBandedLayout, _banded_qr!, _banded_qr, _BandedMatrix, banded_chol!
 
-import LazyBandedMatrices: ApplyBandedLayout, BroadcastBandedLayout, _krontrav_axes, _block_interlace_axes, LazyBandedLayout,AbstractLazyBandedLayout, OneToCumsum
+import LazyBandedMatrices: ApplyBandedLayout, BroadcastBandedLayout, _krontrav_axes, _block_interlace_axes, LazyBandedLayout, AbstractLazyBandedBlockBandedLayout,
+                            AbstractLazyBandedLayout, OneToCumsum, BlockSlice1, KronTravBandedBlockBandedLayout, krontravargs, _broadcast_sub_arguments
 
 import BlockBandedMatrices: _BlockSkylineMatrix, _BandedMatrix, _BlockSkylineMatrix, blockstart, blockstride,
         BlockSkylineSizes, BlockSkylineMatrix, BlockBandedMatrix, _BlockBandedMatrix, BlockTridiagonal,
diff --git a/src/blockbanded/blockbanded.jl b/src/blockbanded/blockbanded.jl
index a362f76..455cc8e 100644
--- a/src/blockbanded/blockbanded.jl
+++ b/src/blockbanded/blockbanded.jl
@@ -74,3 +74,14 @@ BroadcastStyle(::Type{<:PseudoBlockArray{T,N,<:AbstractArray{T,N},<:NTuple{N,Blo
 ###
 
 _krontrav_axes(A::OneToInf{Int}, B::OneToInf{Int}) where N = blockedrange(oneto(length(A)))
+
+
+struct InfKronTravBandedBlockBandedLayout <: AbstractLazyBandedBlockBandedLayout end
+MemoryLayout(::Type{<:KronTrav{<:Any,2,<:Any,NTuple{2,BlockedUnitRange{OneToInfCumsum}}}}) = InfKronTravBandedBlockBandedLayout()
+
+sublayout(::InfKronTravBandedBlockBandedLayout, ::Type{<:NTuple{2,BlockSlice1}}) = BroadcastBandedLayout{typeof(*)}()
+sublayout(::InfKronTravBandedBlockBandedLayout, ::Type{<:NTuple{2,BlockSlice{BlockRange{1,Tuple{OneTo{Int}}}}}}) = KronTravBandedBlockBandedLayout()
+
+copy(M::Mul{InfKronTravBandedBlockBandedLayout, InfKronTravBandedBlockBandedLayout}) = KronTrav((krontravargs(M.A) .* krontravargs(M.B))...)
+
+_broadcast_sub_arguments(::InfKronTravBandedBlockBandedLayout, M, V) = _broadcast_sub_arguments(KronTravBandedBlockBandedLayout(), M, V)
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 7120412..efe13d8 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -100,11 +100,18 @@ include("test_infbanded.jl")
         A = KronTrav(Δ - 2I, Eye(∞))
         @test axes(A, 1) isa InfiniteLinearAlgebra.OneToInfBlocks
         V = view(A, Block.(Base.OneTo(3)), Block.(Base.OneTo(3)))
+        
+        @test MemoryLayout(A) isa InfiniteLinearAlgebra.InfKronTravBandedBlockBandedLayout
         @test MemoryLayout(V) isa LazyBandedMatrices.KronTravBandedBlockBandedLayout
 
+        @test A[Block.(Base.OneTo(3)), Block.(Base.OneTo(3))] isa KronTrav
+
         u = A * [1; zeros(∞)]
         @test u[1:3] == A[1:3, 1]
         @test bandwidths(view(A, Block(1, 1))) == (1, 1)
+
+        @test A*A isa KronTrav
+        @test (A*A)[Block.(Base.OneTo(3)), Block.(Base.OneTo(3))] ≈ A[Block.(1:3), Block.(1:4)]A[Block.(1:4), Block.(1:3)]
     end
 
     @testset "triangle recurrences" begin